Question

A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48°. How tall is the radio tower?

A. 9.82 meters
B. 7.06 meters
C. 6.7 meters
D. 18.65 meters

Answer 1

To find the height of the radio tower, we can use trigonometry and set up equations using the tangent function. The height of the radio tower is approximately 18.65 meters.

Step-by-step explanation:

To find the height of the radio tower, we can use trigonometry.

Let's create a right triangle with the base as the distance from the surveyor to the building (62 meters) and the height as the height of the building.

Using the tangent function, we can set up the following equation:

tan(39°) = (height of building) / 62

Solving for the height of the building, we find:
height of building = 62 * tan(39°)

Now, let's create another right triangle with the base as the distance from the surveyor to the radio tower (62 meters) and the height as the height of the radio tower.

Using the tangent function again, we can set up the following equation:

tan(48°) = (height of radio tower) / 62

Solving for the height of the radio tower, we find:
height of radio tower = 62 * tan(48°)

Therefore, the height of the radio tower is approximately 18.65 meters (Option D).