# Trigonometry Angles Of Elevation And Depression

## Example One - Angle of Elevation

The **Angle of Elevation** is the angle between the horizontal up to the object.

A surveyor standing at the base of a hill, uses a levelling device to see that the top of the hill is at an
**angle of elevation (angle between the horizontal up to the top of the hill) is 37°**.
She then walks up the **slope of hill which she measures at 250 metres**. What is the **vertical height** of the hill?

**Answer:**

sin θ = O/H

sin 37 = x / 250

x = sin 37 × 250

x = 150.45

The vertical height of the hill is **150.45 metres**.

## Did You Know That...?

Stremnaya Road in Bolivia is called the **Death Road**. An estimated 100 travellers each year die on this narrow winding mountain road with steep drops of 4000 metres.

## Example Two - Angle of Depression

The **Angle of Depression** is the angle between the horizontal down to the object.

From the top of a lighthouse, a rescue coordinator can see a rescue boat at an
**angle of depression (angle between the horizontal down to the yacht) of 20°**. He knows the **lighthouse is 28 metres high**.
How **far away from the base of the lighthouse** is the boat?

**Answer:**

*If the angle of depression is 20 degrees, then the inside angle at the top of the triangle is 70 degrees.*

tan θ = O/A

tan 70 = x / 28

x = tan 70 × 28

x = 76.93 metres

The rescue boat is **76.93 metres** away from the base of the lighthouse.

## Question

The **10 metre long** string attached to a kite is at an **angle of elevation (angle between the horizontal ground up to the string) of 60°**.
How **high** is the kite?

**Answer**

8.66 metres