Modeling an angle of elevation | AP Precalculus

Translate an angle of elevation and a horizontal distance into a right triangle.

The angle of elevation is measured upward from the horizontal.
For a vertical height and a horizontal distance, tangent connects the two.
Include any stated eye or instrument height after finding the height difference.

Example 1

Height above the instrument

Find the height of the object to 1 decimal place. An instrument 1.5 m above level ground is 20 m horizontally from a vertical tower. The elevation angle is 35°.

Multiply both sides by

to clear the denominator, which must be non-zero. Collect the

terms to obtain

, then divide both sides by

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Example 2

An instrument is 1.6 m above level ground, 12 m from a vertical tower. The angle of elevation is . Find the height to 1 decimal place.

Multiply both sides by

to clear the denominator, which must be non-zero. Collect the

terms to obtain

, then divide both sides by

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Your turn

Question 1

An instrument is 0 m above level ground, 30 m horizontally from a vertical tower. The angle of elevation to the top is 40°. Find the tower height to 1 decimal place.

Check answer

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 2

An instrument is 1.5 m above level ground, 45 m horizontally from a vertical tower. The angle of elevation to the top is 28°. Find the tower height to 1 decimal place.

Check answer

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 3

An instrument is 1.6 m above level ground, 20 m horizontally from a vertical tower. The angle of elevation to the top is 55°. Find the tower height to 1 decimal place.

Check answer

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 4

An instrument is 0 m above level ground, 50 m horizontally from a vertical tower. The angle of elevation to the top is 35°. Find the tower height to 1 decimal place.

Check answer

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.

Question 5

An instrument is 1.4 m above level ground, 18 m horizontally from a vertical tower. The angle of elevation to the top is 32°. Find the tower height to 1 decimal place.

Check answer

Evaluate in degree mode and keep the full calculator value.

Keep the full value until the final step.

To 1 decimal place.