Question

Charlotte is enjoying a sunny day in the garden on the top of her apartment building. She hears a siren and

is curious where it is coming from. She looks over the edge of the roof and spots an ambulance stopped at
the park down the street from her apartment building. The angle of depression to the ambulance is 3.4°
and her apartment building is 40 feet tall. How far away is the ambulance from the front door of her
apartment building? Round your answer to the nearest tenth. Draw a picture to help you solve the problem.
?

Answer 1

To find the distance from the front door of the apartment building to the ambulance, we can use trigonometry. By applying the tangent function and using the given angle of depression and the height of the building, we can calculate the distance to be approximately 677.9 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometry. Let's draw a diagram to help visualize the situation:

In the diagram, the angle of depression to the ambulance from the edge of the roof is 3.4°. The height of the building is 40 feet. We want to find the distance from the front door of the building to the ambulance.

We can use the tangent function to find the distance. Since we know the height and the angle of depression, we can use the following formula:

tan(angle) = opposite/adjacent

tan(3.4°) = 40/adjacent

Solving for the adjacent side, we get:

adjacent = 40/tan(3.4°)

Using a calculator, we find that the adjacent side is approximately 677.9 feet. Therefore, the ambulance is approximately 677.9 feet away from the front door of the building.