Theory question 110
Trigonometry(a) Given that sin x = 5/13, 0° < x < 90°, find (cos x − 2 sin x)/(2 tan x).
(b) A ladder, LA, leans against a vertical pole at a point L which is 9.6 metres above the ground. Another ladder, LB, 12 metres long, leans on the opposite side of the pole and at the same point L. If A and B are 10 metres apart and on the same straight line as the foot of the pole, calculate, correct to 2 significant figures, the: (i) length of ladder LA; (ii) angle which LA makes with the ground.
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(a) cos x = 12/13, tan x = 5/12
(12/13 − 10/13) ÷ (10/12) = 2/13 × 12/10 = 12/65
(b) Foot of pole to B = √(12² − 9.6²) = √51.84 = 7.2 m; so foot to A = 10 − 7.2 = 2.8 m
(i) LA = √(9.6² + 2.8²) = √100 = 10 m
(ii) tan θ = 9.6/2.8 → θ ≈ 73.7° ≈ 74°
Use a right-angled triangle with sides 5, 12, 13 in (a).