Question

A window in an apartment building is 32m above the ground. From the window, the angle of elevation of the top of the apartment building across the street is 36°. The angle of depression to the bottom of the same apartment building is 47°. Determine the height of the building across the street.

Answer 1

Answer:

y=21.68 building=53.68m

Step-by-step explanation:

Answer 2

Using right triangles, we will see that the building in front is 7.1 meters tall.

How to get the height of the building?

We know that we are on a height of 32m above the ground, and with the angle of 47° we can get the distance between our building and the one in the front, as we already know one cathetus and the adjacent angle to it.

Then we use the relation:

• tan(a) = (opposite cathetus)/(adjacent cathetus)
• tan(47°) = distance/32m
• tan(47°)*32m = distance = 34.32m

Now we can find the difference in height between our position and the top of the other building if we use the 36° angle.

Notice that this is the angle of elevation from the other building, so the adjacent cathetus to it will be the distance between the buildings, which we know measures 34.32m

tan(36°) = H/34.32m

tan(36°)*34.32m = H = 24.9m

This means that the top of the building in the front is 24.9 meters below the window from where we are looking, which is 32 meters above the ground.

32m - 24.9m = 7.1m

We conclude that the building across the street is 7.1 meters tall.

If you want to learn more about right triangles, you can read:

https://brainly.com/question/2217700