(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.
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°)