Question

From points A and B on level ground, the angles of elevation of the top of a building are 25 and 37 respectively. If |AB|=57m calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of the building

Answer 1

Given : From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively.

|AB|=57m

A & B are both on the same side of the building

To find :  the distances of the top of the building from A and B

Solution:

Let say top of Building is C

∠BAC = 25°  => ∠A =  25°

∠ABC = 180° - 37° = 143°  => ∠B =  143°

37° = ∠BAC  + ∠ACB

=> 37° =25°  + ∠ACB

=> ∠ACB = 12° => ∠C =  12°

in Triangle ABC

AB = 57 m

AB/SinC  = BC/SinA  = AC/SinB

=> 57/Sin12° = BC/Sin25°  = AC/Sin 143°

BC =  57 Sin25°/Sin12°  = 115.86  = 116  m

AC =  57 Sin143°/Sin12° = 164.99 = 165 m

AC = 165 m

BC = 116 m

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