An angle of elevation is the angle made at the observer's eye from the horizontal up to an object.

In the diagram below, the angle of elevation from the person's eye to the top of the Eiffel Tower is shown as θ°.

An angle of depression is the angle made at the observer's eye from the horizontal down to an object.

In the diagram below, the angle of depression from the person's eye to the boat is shown as θ°.

Given appropriate measurements, we can use trigonometry to calculate these angles.

**Example** __1__

Fred's eye level is 1.6 metres above ground.

The Eiffel tower is 324 metres tall.

Calculate the angle of elevation, θ°, of the top of the Eiffel Tower when Fred is 550 metres away.

**Answer 1**

In relation to the angle shown as θ°, the opposite side of the right-angled triangle has length 324 - 1.6 = 322.4 m and the adjacent side is 550 m.

Thus, tan θ° = 322.4 ÷ 550 = 0.58618...

θ° = tan^{-1}(0.58618) = **30.4°**

**Example** __2__

Fred's eye level is 1.6 metres above ground.

He is standing on cliff which is 30 metres above sea level and measures the angle of depression to a boat as 31°.

Calculate the horizontal distance, d, from Fred to the boat.

**Answer 2**

In relation to the 31° angle of depression, the opposite side of the right-angled triangle has length 30 + 1.6 = 31.6 m and the adjacent side is d m.

Thus, tan 31° = 31.6 ÷ d

d = 31.6 ÷ tan 31° = **52.6 m**