If we label
T = top of tower
P = base of tower
h = PT = height of tower
h/64 = tan30°
using the law of cosines,
PB^2 = 64^2 + 58^2 - 2*64*58 cos50°
now you want θ = ∡PBT, so
h/PB = tanθ
the base of vertical mast is on the same level ground with two points A and B. from the point A, 64m south of the mast, the angle of elevation of the top of the mast is 30⁰. B is 58m from A on a bearing of 050⁰. find correct to 3 s.f, the height of the tower. calculate, correct to the nearest degree, the angle of depression of B from the top of the tower.
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