Question

A man standing on a cliff observes the top of a tower at an angle of elevation of 45⁰ and the foot of the tower at an angle of depression of 30⁰. If the tower is 120 meters away from the man, then what is the height of the tower in meters?​

Answer 1

Let's first draw a diagram to understand the problem better:

A (top of tower)
/|
/ |
/ | x (height of tower)
120m / |
/ |
/ |
/ |
/θ /
C (man) --------
30°
In the diagram, A represents the top of the tower, C represents the man, and x represents the height of the tower that we want to find. θ represents the angle of elevation of A as observed from C.

We know that tan θ = x/120 (since tangent is opposite over adjacent), and we also know that tan 45⁰ = 1 (since tangent of 45⁰ is equal to 1). Thus, we have:

tan 45⁰ = x/120
1 = x/120
x = 120

So, the height of the tower is 120 meters.