# Angles of elevation and depression

If a person stands and looks up at an object, the angle of elevation is the angle between the horizontal line of sight and the object.

If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object.

Trigonometry can be used to solve problems that use an angle of elevation or depression.

### Example

An architect wants to calculate the height of a building. He stands 50 m away from the base of the building and looks up at the top of the building. The angle of elevation from the architect to the top of the building is 70°. Calculate the height of the building. Give the answer to one decimal place.

Label the sides of the triangle , and .

Next choose the correct ratio from .

In the triangle the length is known and the length must be calculated.

Use  Make the subject by multiplying both sides by 50.  The building is 137.4 m tall.

Question

From the top of a 72 m high vertical cliff, a boat has an angle of depression of 32°. How far is the boat from the base of the cliff? Give the answer to 1 decimal place.

In the triangle the length is known and the length must be calculated.

Use  Rearrange the equation to make the subject.

Multiply both sides by . Divide both sides by .  The boat is 115.2 m from the base of the cliff.