Question

a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?

Answer 1

To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.

Step-by-step explanation:

To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:

1. Tan(39°) = Height of Building / 64 meters
2. Height of Building = 64 meters * Tan(39°)

After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:

1. Tan(48°) = Total Height / 64 meters
2. Total Height = 64 meters * Tan(48°)

Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.

Height of Radio Tower = Total Height - Height of Building

By following these steps, we can calculate the height of the radio tower.

Answer 2

The distance of the observer and height of the building form a right angle triangle. Using:
tan∅ = height/base
We calculate the height of the building:
height = 64tan(39)
height = 51.8 meters

The second angle is obtained when the height of both the building and tower are used:
Height(building + tower) = 64tan(48)
51.8 + tower height = 71.1
tower height = 19.3 meters