(a) Given that \(\cos x = 0.7431, 0° < x < 90°\), use tables to find the values of : (i) \(2 \sin x\) ; (ii) \(\tan \frac{x}{2}\). (b) The interior angles o...
Question 1 Report
(a) Given that \(\cos x = 0.7431, 0° < x < 90°\), use tables to find the values of : (i) \(2 \sin x\) ; (ii) \(\tan \frac{x}{2}\).
(b) The interior angles of a pentagon are in ratio 2 : 3 : 4 : 4 : 5. Find the value of the largest angle.
Answer Details
(a) Since \(\cos x = 0.7431\) and \(0^\circ < x < 90^\circ\), from tables \(x = 42^\circ\).
(i) \(\sin42^\circ = 0.6691\), so
\[2\sin x = 2\times0.6691 = 1.338.\]
(ii) \(\dfrac{x}{2} = 21^\circ\), so
\[\tan\frac{x}{2} = \tan21^\circ = 0.3839.\]
(b) The five interior angles of a pentagon sum to \((5-2)\times180^\circ = 540^\circ\). With ratio \(2:3:4:4:5\), the total number of parts is \(2+3+4+4+5 = 18\).
\[\text{One part} = \frac{540^\circ}{18} = 30^\circ.\]
\[\text{Largest angle} = 5\times30^\circ = 150^\circ.\]
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