JAMB UTME - Mathematics - 1983

PQRS is a desk of dimensions $2\text{m} \times 0.8$ which is inclined at $30^\circ$ to the horizontal. Find the inclination of the diagonal PR to the horizontal

30

^{\circ}

35'

30

^{\circ}

32'

15

^{\circ}

36'

10

^{\circ}

42'

Antwortdetails

tan $θ$ = $\frac{0.8}{2}$ = (0.4)

$θ$ = tan-1(0.4)

From the diagram, the inclination of the diagonal PR to the horizontal is 10 $^{\circ}$ 42'

Lies die Unterrichtsnotiz zu Measures Of Dispersion (JAMB)

Measures Of Dispersion

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Frage 4 Bericht

On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram. correct to 3 significant figures.

6.00cm2

6.10cm2

6cmv

6.09cm2

4.00cm2

Coordinate Geometry

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Frage 5 Bericht

PQRS is a cyclic quadrilateral. If ∠QPS = 75o, what is the size of ∠QRS?

180o

150o

105o

75o

Circles

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Frage 6 Bericht

If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?

4:1 increase

2:1 increase

1:1 no change

1:4 decrease

3:4 decrease

Variation

Progression

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Frage 7 Bericht

The farm yield of four crops on a piece of land in Ondo are represented on the pie chart. what is the angle of the sector occupies by Okro in the chart?

11

^{\circ}

19

\frac{1}{3}

^{\circ}

33

\frac{1}{3}

^{\circ}

91

\frac{1}{3}

^{\circ}

91

^{\circ}

Antwortdetails

Adding the values of all the items together, it gives 70

Okro sector = $\frac{145}{270}$ x $\frac{360^{o}}{1}$

= 19.33 $^{\circ}$

= 19 $\frac{1}{3}$ $^{\circ}$

Lies die Unterrichtsnotiz zu Angles (WAEC)

Angles

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Frage 8 Bericht

The value of $ (0.303)^3 - (0.02)^3 $ is

0.019

0.0019

0.00019

0.000019

0.0278

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Frage 9 Bericht

If $0.0000152 \times 0.042 = A \times 10^8$, where $1 \le A < 10$, find A and B

A = 9, B = 6.38

A = 6.38, B = -9

A = -6.38, B = -9

A = -9, B = -6.38

Antwortdetails

0.0000152 x 0.042 = A x 108

1 $\leq$ A < 10, it means values of A includes 1 - 9

0.0000152 = 1.52 x 10-5

0.00042 = 4.2 x 10-4

1.52 x 4.2 = 6.384

10-5 x 10-4

= 10-5-4

= 10-9

= 6.38 x 10-9

A = 6.38, B = -9

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Statistics

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Frage 10 Bericht

Solve the following equations 4x - 3 = 3x + y = x - y = 3, 3x + y = 2y + 5x - 12

x = 5, y = 2

x = 2, y = 5

x = 5, y = -2

x = -2, y = -5

x = -5, y = -2

Solution Of Linear Equations

Algebraic Expressions

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Frage 11 Bericht

Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures

4.46

4.48

4.47

4.49

4.50

Fractions, Decimals And Approximations

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Frage 12 Bericht

The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel

7

13

5

13

6

13

8

13

4

13

Probability

Surds (radicals)

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Frage 13 Bericht

y varies partly as the square of x and partly as the inverse of the square root of x. Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4.

y = $\frac{10 x^{2}}{31} + \frac{52}{31 \sqrt{x}}$

y = x2 + $\frac{1}{\sqrt{x}}$

y = x2 + $\frac{1}{x}$

y = $\frac{x^{2}}{31} + \frac{1}{31 \sqrt{x}}$

Antwortdetails

y = kx2 + $\frac{c}{\sqrt{x}}$
y = 2 when x = 1
2 = k + $\frac{c}{1}$
k + c = 2
y = 6 when x = 4
6 = 16k + $\frac{c}{2}$
12 = 32k + c
k + c = 2
32k + c = 12
= 31k + 10
k = $\frac{10}{31}$
c = 2 - $\frac{10}{31}$
= $\frac{62 - 10}{31}$
= $\frac{52}{31}$
y = $\frac{10 x^{2}}{31} + \frac{52}{31 \sqrt{x}}$

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

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Frage 14 Bericht

Given that cos z = L , whrere z is an acute angle, find an expression for $ \frac{\cot z - \cosec z}{\sec z + \tan z} $

1-L

1+L

L²√3

1+L

1+L³

L²

L(L−1)

1−L+1√1−L²

Antwortdetails

Given Cos z = L, z is an acute angle
$\frac{cot z - cosec z}{sec z + tan z}$ = cos z
= $\frac{cos z}{sin z}$
cosec z = $\frac{1}{sin z}$
cot z - cosec z = $\frac{cos z}{sin z}$ - $\frac{1}{sin z}$
cot z - cosec z = $\frac{L - 1}{sin z}$
sec z = $\frac{1}{cos z}$
tan z = $\frac{sin z}{cos z}$
sec z = $\frac{1}{cos z}$ + $\frac{sin z}{cos z}$
= $\frac{1}{l}$ + $\frac{sin z}{L}$
the original eqn. becomes
$\frac{cot z - cosec z}{sec z + tan z}$ = $\frac{L - \frac{1}{sin z}}{1 + s i n \frac{z}{L}}$
= $\frac{L (L - 1)}{sin z (1 + sin z)}$
= $\frac{L (L - 1)}{sin z + 1 - c o s^{2} z}$
= sin z + 1
= 1 + $\sqrt{1 - L^{2}}$
= $\frac{L (L - 1)}{1 - L + 1 \sqrt{1 - L^{2}}}$

Lies die Unterrichtsnotiz zu Matrices And Determinants (JAMB)

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Matrices And Determinants

Modular Arithmetic

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Frage 15 Bericht

If w varies inversely as V and U varies directly as w3, Find the relationship between u and v given that u = 1, when v = 2

u =

\frac{8}{v^{3}}

v =

\frac{8}{u^{2} v^{3}}

u = 8v3

v = 8u2

Antwortdetails

W $α$ $\frac{1}{v}$ u $α$ w3
w = $\frac{k_{1}}{v}$
u = k2w3
u = k2( $\frac{k_{1}}{v}$ )3
= $\frac{k_{2} k_{1}^{2}}{v^{3}}$
k = k2k1k2
u = $\frac{k}{v^{3}}$
k = uv3
= (1)(2)3
= 8
u = $\frac{8}{v^{3}}$

Lies die Unterrichtsnotiz zu Variation (WAEC)

Lies die Unterrichtsnotiz zu Change Of Subject Of A Formula/Relation (WAEC)

Variation

Change Of Subject Of A Formula/Relation

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Frage 16 Bericht

The scores of set of final year students in the first semester examination in a paper are 41, 29, 55, 21, 47, 70, 70, 40, 43, 56, 73, 23, 50, 50. Find the median of the scores.

47

50

48

\frac{1}{2}

48

49

Antwortdetails

By re-arranging 21, 23, 29, 40, 41, 43| 47, 50| 50, 55, 56, 70, 70, 73
The median = $\frac{47 + 50}{2}$
$\frac{97}{2}$
= 48 $\frac{1}{2}$

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Frage 17 Bericht

Given a regular hexagon, calculate each interior angle of the hexagon

60o

30o

120o

45o

135o

Antwortdetails

Sum of interior angles of polygon = (2n - 4)rt < s

sum of interior angles of an hexagon
(2 x 6 - 4) x 90o = (12 - 4) x 90o
= 8 x 90o
= 720o
each interior angle will have $\frac{720^{o}}{6}$
= 120o

Lies die Unterrichtsnotiz zu Angles (WAEC)

Angles

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Frage 18 Bericht

In the figure, find PRQ

66

\frac{1}{2}

^{\circ}

^{\circ}

125

^{\circ}

105

^{\circ}

65

^{\circ}

Antwortdetails

Angle subtended at any part of the circumference of the circle $\frac{125^{o}}{2}$ at centre = 360 $^{\circ}$ - 235 $^{\circ}$ = 125 $^{\circ}$

$\bar{P Q R}$ = $\frac{125}{2}$

= 62 $\frac{1}{2}$ $^{\circ}$

Lies die Unterrichtsnotiz zu Representation Of Data (JAMB)

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Representation Of Data

Triangles And Polygons

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Frage 19 Bericht

If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement?

55

10

5

4

2

Antwortdetails

% error = $\frac{Actual error}{real value}$ x 100
= $\frac{5}{250}$ x 100
= 2

Lies die Unterrichtsnotiz zu Percentages (WAEC)

Percentages

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Frage 20 Bericht

The figure FGHK is a rhombus. What is the value of angle X?

30

^{\circ}

90

^{\circ}

150

^{\circ}

120

^{\circ}

60

^{\circ}

Antwortdetails

< HKF = 60 $^{\circ}$ , < KFG = 120 $^{\circ}$

< KFG = < KHG = x(opposite angles)

x = 120 $^{\circ}$

Lies die Unterrichtsnotiz zu Angles (WAEC)

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

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Frage 21 Bericht

Solve the simultaneous equations for x in x2 + y - 8 = 0, y + 5x - 2 = 0

-28, 7

6, -28

6, -1

-1, 7

3, 2

Solution Of Linear Equations

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Frage 22 Bericht

One interior angle of a convex hexagon is 170o and each of the remaining interior angles is equal to xo. Find x

120o

110o

105o

102o

100o

Antwortdetails

An hexagon polygon is a six sided polygon
n = 6
sum of all interior angles of hexagon polygon will be (2n - 4) x 90o
= [2 x 6 - 4] x 90
= 720o
If one angle is 170o and each of the remaining five angles is 5xo
5xo + 170o = 720o
= 5x + 550
x = $\frac{550}{5}$
= 110o

Lies die Unterrichtsnotiz zu Polynomials (JAMB)

Polynomials

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Frage 23 Bericht

Simplify $ \frac{3}{2x-1} + \frac{2-x}{x-2} $

2−x

(2x−1)(x−2)

5−x

(2x−1)(x−2)

4−2x

2x−1

6−3x

(2x−1)(x−2)

Antwortdetails

$\frac{3}{2 x - 1}$ + $\frac{2 - x}{x - 2}$
= $\frac{3}{2 x - 1}$ - $\frac{x - 2}{x - 2}$
= $\frac{3}{2 x - 1}$ - 1
= $\frac{3 - (2 x - 1)}{2 x - 1}$
= $\frac{3 - 2 x + 1}{2 x - 1}$
= $\frac{4 - 2 x}{2 x - 1}$

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 24 Bericht

Find the missing value in the following table:

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y=x^3-x+3$		$3$	$3$	$3$	$9$	$27$

-3

3

-9

13

9

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Frage 25 Bericht

If M represents the median and D the mode of the measurements 5, 9, 3, 5, 7, 5, 8, then (M, D) is

(6, 5)

(5, 8)

(5, 7)

(5, 5)

(7, 5)

Probability

Linear Inequalities

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Frage 26 Bericht

The lengths of the sides of a right angled triangle are (3x + 1)cm, (3x - 1)cm and xcm. Find x

2

6

18

12

5

Algebraic Expressions

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Frage 27 Bericht

A construction company is owned by two partners X and Y and it is agreed that their profit will be divided in the ratio 4:5. At the end of the year, Y received ₦5,000 more than X. What is the total profit of the company for the year?

₦20, 000

₦25,000

₦30,000

₦15,000

₦45, 000

Sine, Cosine And Tangent Of An Angle

Ratio, Proportions And Rates

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Frage 28 Bericht

If x + 2 and x - 1 are factors of the expression 1x3 + 2kx2 + 24, find the values of 1 and K

1 = -6, k = -9

1 = -2, k = 1

k = -1, 1 = -2

1 = 0, k = 1

k = 0,1 = 6

Algebraic Expressions

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Frage 29 Bericht

A man drove for 4 hours at a certain speed, he then doubled his speed and drove for another 3 hours. Although he covered 600 kilometers. At what speed did he drive for the last 3 hours?

120km/hr

60km/hr

670km/hr

40km/hr

Antwortdetails

Speed = $\frac{d i s t a n c e}{t i m e}$
let x represent the speed, d represent distance
x = $\frac{d}{4}$
d = 4x
2x = $\frac{600 - d}{3}$
6x = 600 - d
6x = 600 - 4x
10x = 600
x = $\frac{600}{10}$
= 60km/hr

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Frage 30 Bericht

Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26

15o, 25o, 35o, 40o, 65o

60o, 100o, 140o, 160o, 260o

6o, 10o, 14o, 16o, 26o

30o, 50o, 70o, 80o, 130o

none of the above

Antwortdetails

6 + 10 + 14 + 16 + 26 = 72
$\frac{6}{72}$ x 360
= 30o
Similarly others give 30o, 50o, 70o, 80o and 130o respectively

Lies die Unterrichtsnotiz zu Polynomials (JAMB)

Lies die Unterrichtsnotiz zu Measures Of Dispersion (JAMB)

Polynomials

Measures Of Dispersion

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Frage 31 Bericht

Find x if (xbase4)2 = 100100base2

6

12

100

210

110

Antwortdetails

(x2)4 to base10 gives (1 x 25) + (1 x 25) + (1 x 2)
32 + 4 = 36
x2 = 36, x = 6
610 to base 4 = $\begin{array}{cc} 4 & 6 \\ 1 r 2 \end{array}$
= 124

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 32 Bericht

In the figure PT is a tangent to the circle with centre at O. If PQT = $30^\circ$, find the value of PTO

30

^{\circ}

50

^{\circ}

24

^{\circ}

12

^{\circ}

60

^{\circ}

Antwortdetails

FROM the diagram, PQT = 50 $^{\circ}$

PTQ = 50 $^{\circ}$ (opposite angles are supplementary)

Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 33 Bericht

Simplify $ \log_{10} a^{\frac{1}{3}} + \frac{1}{4}\log_{10} a - \frac{1}{12}\log_{10} a^{7} $

1

\frac{7}{6}

log10 a

zero

10

Antwortdetails

log10 a $\frac{1}{3}$ + $\frac{1}{4}$ log10 a - $\frac{1}{12}$ log10a7 = log10 a $\frac{1}{3}$ + log10 $\frac{1}{4}$ - log10 a $\frac{7}{12}$
= log10 a $\frac{7}{12}$ - log10 a $\frac{7}{12}$
= log10 1 = 0

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Logarithms

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Frage 34 Bericht

A ship H leaves a port P and sails 30 km due south. Then it sails 50km due west. What is the bearing of H from P

20o 34'

243o 26'

116o 34'

63o 26'

240o 56'

Bearings

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Frage 35 Bericht

In a sample survey of a University Community, the following table shows the percentage distribution of the number of members per household:

No. of members per household	1	2	3	4	5	6	7	8	Total
No. of households	3	12	15	28	21	10	7	4	100

What is the median?

4

3

5

4.5

none

Antwortdetails

$\begin{array}{cc} x & f \\ 1 & 3 \\ 2 & 13 \\ 3 & 15 \\ 4 & 28 \\ 5 & 21 \\ 6 & 10 \\ 7 & 7 \\ 8 & 4 \end{array}$
Median is half of total frequency = 50th term
4 falls in the range = 4

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Frage 36 Bericht

In the figure, PQR is a straight line. Find the values of x and y.

^{\circ}

x = 15

^{\circ}

, y = 52.5

^{\circ}

x = 22.5

^{\circ}

, y = 45.0

^{\circ}

x = 56.25

^{\circ}

, y = 11.5

^{\circ}

Antwortdetails

$\frac{2}{3}$ + 3y + 45 $^{\circ}$ = 180 $^{\circ}$

3x + 6y + 90 $^{\circ}$ = 360 $^{\circ}$

3x + 67 = 270.......(i) x 2, 5x + y + y = 180 $^{\circ}$

5x + 2y = 180 $^{\circ}$ .......(ii) x 6

6 x 12y = 540..........(iii)

30x + 12y = 1080.........(iv)

egn(iv) - eqn(iii)

24x = 540

x = 22.5 and y = 33.75 $^{\circ}$

Antwort anzeigen

Frage 37 Bericht

In a figure, PQR = 60o, PRS = 90o, RPS = 45o, QR = 8cm. Determine PS

2

\sqrt{3}

cm

4

\sqrt{6}

cm

2

\sqrt{6}

cm

8

\sqrt{6}

cm

8cm

Antwortdetails

From the diagram, sin 60o = $\frac{P R}{8}$
PR = 8 sin 60 = $\frac{8 \sqrt{3}}{2}$
= 4 $\sqrt{3}$
Cos 45o = $\frac{P R}{P S}$ = $\frac{4 \sqrt{3}}{P S}$
PS Cos45o = 4 $\sqrt{3}$
PS = 4 $\sqrt{3}$ x 2
= 4 $\sqrt{6}$

Lies die Unterrichtsnotiz zu Circles (WAEC)

Lies die Unterrichtsnotiz zu Angles Of Elevation And Depression (WAEC)

Lies die Unterrichtsnotiz zu Areas (WAEC)

Lies die Unterrichtsnotiz zu Angles (WAEC)

Circles

Angles Of Elevation And Depression

Areas

Angles

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Frage 38 Bericht

Find the mean of the following 24.57, 25.63, 24.32, 26.01, 25.77

25.12

25.30

25.26

25.50

25.75

Antwortdetails

$\frac{24.57 + 25.63 + 24.32 + 26.01 + 25.77}{5}$
mean = $\frac{126.3}{5}$
= 25.26

Lies die Unterrichtsnotiz zu Integration (JAMB)

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Integration

Statistics

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Frage 39 Bericht

Which of the following equations represents the graph above?

y = 2 + 7x + 4x2

y = 2 - 7x + 4x2

y = 2 + 7x - 4x2

y = 2 - 7x - 4x2

Antwortdetails

x = -2 or x = $\frac{1}{4}$

(x + 2)(4x - 1) = 0

y = 2 - 7x - 4x2

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 40 Bericht

Make T the subject of the equation $ \frac{av}{1-v} = \sqrt{\frac{2v+T}{a+2T}} $

T = $\frac{3 a v}{1 - v}$

T = $\frac{1 + v}{2 a^{2} v^{3}}$

T = $\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} + (1 - v)^{2}}$

\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} - (1 - v)^{3}}

Antwortdetails

$\frac{a v}{1 - v}$ = $\sqrt{\frac{2 v + T}{a + 2 T}}$
$\frac{(a v)^{3}}{(1 - v)^{3}}$ = $\frac{2 v + T}{a + 2 T}$
$\frac{a^{3} v^{3}}{(1^{3} - v)^{3}}$ = $\frac{2 v + T}{a + 2 T}$
= $\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} - (1 - v)^{3}}$

Lies die Unterrichtsnotiz zu Variation (WAEC)

Lies die Unterrichtsnotiz zu Change Of Subject Of A Formula/Relation (WAEC)

Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Variation

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Quadratic Equations

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Frage 41 Bericht

If $ \left(\frac{2}{3}\right)^m \left(\frac{3}{4}\right)^n = \frac{252}{729} $, find the values of m and n

m = 4, n = 2

m = -4, n = -2

m = -4, n =2

m = 4, n = -2

m = -2, n = 4

Antwortdetails

( $\frac{2}{3}$ )m ( $\frac{3}{4}$ )n = $\frac{252}{729}$
$\frac{2^{m}}{4^{n}}$ x $\frac{3^{n}}{3^{m}}$ = 283-6
2m - 2n x 3n - m = 28 x 3-6
m - 2n = 8........(i)
-m + n = -6........(ii)
Solving the equations simultaneously
m = 4, n = -2

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 42 Bericht

Simplify $ \frac{3\sqrt{27a^{-9}}}{8} $

9a²

2a³

3

2a³

2

3a²

2

Antwortdetails

$\frac{3 \sqrt{27 a^{- 9}}}{8}$ = $\frac{3 a^{- 3}}{2}$
= $\frac{3}{2}$ x $\frac{1}{a^{3}}$
= $\frac{3}{2 a^{3}}$

Lies die Unterrichtsnotiz zu Fractions, Decimals And Approximations (WAEC)

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Fractions, Decimals And Approximations

Surds (radicals)

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Frage 43 Bericht

The scores of 16 students in a mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65,
70. What is the sum of the median and modal scores?

125

130

140

150

Measures Of Dispersion

Statistics

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Frage 44 Bericht

In a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography and Additional mathematics is as shown in the pie chart. How many pupils offer Additional Mathematics?

15

10

18

12

20

Antwortdetails

2x - 24) $^{\circ}$ + (3x - 18) $^{\circ}$ + (2x + 12) $^{\circ}$ + (x + 12) $^{\circ}$ + x $^{\circ}$ = 360 $^{\circ}$

9x = 360 $^{\circ}$ + 18 $^{\circ}$

x = $\frac{378}{9}$

= 42 $^{\circ}$ , if x = 42 $^{\circ}$ , then add maths = $\frac{2 x - 42}{360}$ x 60

= $\frac{2 \times 42 - 24}{360}$ x 60

= $\frac{84 - 24}{6}$

= 10

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Statistics

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Frage 45 Bericht

PQR is the diagram of a semicircle RSP with centre at Q and radius of length 3.5cm. If QPT = 60^o. Find the perimeter of the figure PTRS. $ \pi = \frac{22}{7} $

25cm

18cm

36cm

29cm

25.5cm

Antwortdetails

Circumference of PRS = $\frac{π}{2}$ = $\frac{22}{7}$ x $\frac{7}{1}$ x $\frac{1}{2}$
= 11cm
Side PT = 7cm, Side TR = 7cm
Perimeter(PTRS) = 11cm + 7cm + 7cm
= 25cm

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Frage 46 Bericht

If O is the centre of the circle in the figure, find the value of x

50

260

100

65

130

Antwortdetails

From the diagram; The value of x = 360 $^{\circ}$ - 2(130 $^{\circ}$ )

= 360 - 260

= 100 $^{\circ}$

Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 47 Bericht

In a triangle PQT, QR = $ \sqrt{3}\text{ cm} $, PR = 3cm, PQ = $ 2\sqrt{3} $cm and PQR = 30^o. Find angles P and R

P = 60o and R = 90o

P = 30o and R = 120o

P = 90o and R = 60o

P = 60o and R 60o

P = 45o and R = 105o

Antwortdetails

By using cosine formula, p2 = Q2 + R2 - 2QR cos p
Cos P = $\frac{Q^{2} + R^{2} - p^{2}}{2 Q R}$
= $\frac{(3)^{2} + 2 (\sqrt{3})^{2} - 3^{2}}{2 \sqrt{3}}$
= $\frac{3 + 12 - 9}{12}$
= $\frac{6}{12}$
= $\frac{1}{2}$
= 0.5
Cos P = 0.5
p = cos-1 0.5 = 60 $^{\circ}$
= < P = 60 $^{\circ}$
If < P = 60 $^{\circ}$ and < Q = 30

< R = 180 $^{\circ}$ - 90 $^{\circ}$
angle P = 60 $^{\circ}$ and angle R is 90 $^{\circ}$

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Frage 48 Bericht

PQRS is a cyclic quadrilateral which PQ = PS. PT is a tangent to the circle and PQ makes an angle of $50^\circ$ with the tangent as shown in the figure. What is the size of QRS?

50