Math

from a spot 60 ft from the base of a building the angle of elevation is 48 degrees and the of elevation of the top of the antenna is 56 degrees. What is the height of the building? What is the height of the antenna?

From your school subject line, I assumed you were studying history or religion.

Why didn't you type Math in the School Subject box?

tan 48 = height of building/60

tan 56 = height of top of antenna/60
if you want the height of the antenna itself, subtract.

To find the height of the building and the height of the antenna, we can use the properties of trigonometry.

Let's first define the variables:
- Let h be the height of the building.
- Let a be the height of the antenna.

Now, let's consider the triangle formed by the spot, the top of the building, and the top of the antenna.

Since the angle of elevation from the spot to the top of the building is 48 degrees, we can use the tangent function to determine the height of the building:

tan(48 degrees) = h / 60 ft

To find h, we can rearrange the equation:

h = tan(48 degrees) * 60 ft

We can then use a calculator to find the value of tan(48 degrees) and multiply it by 60 ft to find the height of the building.

Now, let's consider the angle of elevation from the spot to the top of the antenna, which is 56 degrees.

Using the tangent function again, we can find the height of the antenna:

tan(56 degrees) = a / 60 ft

Rearranging the equation, we have:

a = tan(56 degrees) * 60 ft

We can calculate the value of tan(56 degrees) and multiply it by 60 ft to find the height of the antenna.

By following these calculations, we can determine the height of the building and the height of the antenna.