(a) Given that cos x = 0.7431, 0° < x < 90°, use tables to find the values of : (i) 2sin 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.
Explanation
(a) \(\cos x = 0.7431\)
\(x = \cos^{-1} (0.7431)\)
\(x = 42°\)
(i) \(2 \sin x = 2 \sin 42\)
= \(2 \times 0.6692\)
= \(1.3384\)
(ii) \(\tan \frac{x}{2} = \tan \frac{42}{2}\)
= \(\tan 21°\)
= \(0.3839\)
(b) Sum of the interior angles of a polygon = \((2n - 4) \times 90°\)
For a pentagon, n = 5
\((2(5) - 4) \times 90° = 6 \times 90°\)
= \(540°\)
Ratio of sides = 2:3:4:4:5
Total = 2 + 3 + 4 + 4 + 5 = 18
Largest angle = \(\frac{5}{18} \times 540° = 150°\)