angle of depression

Question

Sherlock Holmes, who is on the roof of the hospital that is 40 meters tall, spots John Watson on the street at an angle of depression of 50°. How far away is Watson from the hospital?

Answer 1

The building forms a right triangle with the street. The building is 40m in height, and the angle from the top of the building to the place where John Watson is standing is 50o.

 

The solution is provided by the tangent of the angle. Tangent is defined as the ratio of the side opposite the angle divided by the side adjacent to the angle.

 

In this case, let x = the length of the opposite side.

 

So, x ÷ 40m = tan 50^o

 

x  = tan 50^o times 40m; the tangent of 50^o ≅ 1.2

 

x ≅ 1.2 times 40m

 

x ≅ 48m