Question: Learning Goal I can use trigonometry to determine the measure of an angle, the length of a side,…

Learning Goal

I can use trigonometry to determine the measure of an angle, the length of a side, and solve a right triangle.

10. A building is 45 feet tall. The angle of depression from the top of the building to a person on the ground is 38°. How far is the person from the building?

[Diagram of a building with a height of 45 ft and an angle of depression of 38° to a person on the ground, labeled as “d”.]

Solution

To find how far the person is from the building, we can use the tangent trigonometric function. The angle of depression from the top of the building to the person on the ground is 38°, and the height of the building is 45 feet. The distance \( d \) from the building can be found using the tangent of the angle: The tangent of an angle in a right triangle is the opposite side over the adjacent side. \[ \tan(38^\circ) = \frac{45}{d} \] Rearrange the equation to solve for \( d \): \[ d = \frac{45}{\tan(38^\circ)} \] Calculate \( d \): Using a calculator, find \( \tan(38^\circ) \). \[ \tan(38^\circ) \approx 0.7813 \] Now calculate \( d \): \[ d = \frac{45}{0.7813} \approx 57.6 \] So, the person is approximately 57.6 feet from the building.