Question

The feet of two vertical poles of heights 3metres and 7metres are in line with a point P on the ground, the smaller pole being between the taller pole and P at a distance 20metres from P. The angle of elevation of the top (T) of the taller pole from the top (R) of the smaller pole is 30◦. Calculate the: (i) distance RT (ii) distance of the foot of the taller pole from P, correct to 3s.fs. (iii) angle of elevation of T from P, correct to 1d.p. Please with full and well detailed solution

Answer 1

(i) Distance RT

Let RT = x

Using the cosine rule,

x² = 20² + 7² - 2(20)(7)cos30°

x² = 400 + 49 - 280cos30°

x² = 449 - 140

x = √309

RT = 17.6m

(ii) Distance of the foot of the taller pole from P

Let TP = y

Using the cosine rule,

y² = 20² + 3² - 2(20)(3)cos30°

y² = 400 + 9 - 120cos30°

y² = 409 - 72

y = √337

TP = 18.3m

(iii) Angle of elevation of T from P

Let ∠TPT = θ

Using the sine rule,

sinθ = (7/18.3)sin30°

sinθ = 0.38

θ = 22.3°