Trigonometry Question (With Answer)

A building AB, located on the top of a terrace, is 50m high. From a point C on the ground, the angles of elevation of the top A and the base B of the building are 42 degrees and 27 degrees respectively. Find
(a) the distance AC,
(b) the horizontal distance from C to the building,
(c) the height of the terrace.

Answer:
First, we need to build the triangle to represent the one in the diagram, with all the related angles that can be found stated.

a) Using Sine Rule:


b) the horizontal distance from C to the building = CD

Hence, the horizontal distance from C to the building = 128m

c) height of the terrace = BD


Hence, the height of the terrace = 65.2m