Find the value of ? ? in the diagram

Assessment: JAMB UTME - Mathematics - 2001 Subject: General Mathematics

Question 1 Report

Find the value of $θ$ in the diagram

60

^{\circ}

100

^{\circ}

120

^{\circ}

30

^{\circ}

Answer Details

Using cosine formula (t $\sqrt{3}$ )2 = t2 + t2 - 2t2 cos $θ$

3t2 = 2t2 - 2t2 cos $θ$ = 2t2(1 - cos $θ$ )

1 - cos $θ$ = $\frac{3 t^{2}}{2 t^{2}}$ = $\frac{3}{2}$

cos = 1 - $\frac{3}{2} = - \frac{1}{2}$

$θ$ = cos-1(- $\frac{1}{2}$ ) = 120 $^{\circ}$ and 240 $^{\circ}$

N.B 0 $\geq$ $θ$ 360

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