Approximate the height of the building.....

Question

from a point A that is 10 meters above level ground, the angle of elevation of the top of a building is 42 degrees and the angle of depression of the base of the building is 8 degrees. Approximate the height of the building.

Answer 1

Draw label a sketch for reference.

 

We can find the distance from Point A to the building by

 

d = 10 / tan(8°) = 71.2 m

 

 

Now that we know d, we can find h₂, the height above Point A.  The height of the building is h = h₁ + h₂.

 

 

h₁ is given by 10 m.

 

h₂ = d tan(42°) = 71.2 tan(42°) = 64.1 m

 

 

The height of the building is 10 + 64.1 = 74.1 m