Theory question 102
Trigonometry(a) Given that cos x = 0.7431, 0 < x < 90°, use tables to find the values of (i) 2 sin x; (ii) tan (x/2)
(b) The interior angles of a pentagon are in ratio 2 : 3 : 4 : 4 : 5. Find the value of the largest angle.
Show the model answer
Model answer
(a) cos x = 0.7431 gives x = 42°.
(i) 2 sin 42° = 2 × 0.6691 = 1.3382.
(ii) tan 21° = 0.3839.
(b) Angles of a pentagon add to 540°. Ratio total = 18, so the largest angle = 5/18 × 540° = 150°.
Explanation
Find x from the cosine table first, then use it for the other ratios.