From the top of a building 100m high, the angle of depression of a point A due to East of it is 30 degrees. From a point B duo South of the building, the angle of elevation of the top is 60 degrees. Find the distance AB

Guest Mar 2, 2017

#1**0 **

From the top of a building 100m high, the angle of depression of a point A due to East of it is 30 degrees. From a point B duo South of the building, the angle of elevation of the top is 60 degrees. Find the distance AB

Distance to A from the building = 100m/ tan 30 = 100√ 3 m

Distance to B from building = 100m / tan 60 = 100 / √ 3 m

A and B are at right angles........so the distance between them forms the hypotenuse of a right triangle......so we have

AB = √ [ (100√ 3)^2 + (100/√ 3)^2 ] = 100√ [3 + 1/3] m ≈ 182.57 m

CPhill
Mar 2, 2017