How to Calculate the Height of a Tower Using Trigonometry

Question:

A wire 100 feet long is attached to the top of a radio transmission tower, making an angle of 43° with the ground. How high is the tower, in feet?

Answer:

The height of the tower is approximately 68.2 feet.

To determine the height of the tower, we can use trigonometry. Let's call the height of the tower 'h'. Since the wire is attached to the top of the tower and makes an angle of 43° with the ground, we can use the sine function:

sin(43°) = h/100

Solving for 'h', we get: h = 100*sin(43°)

Using a calculator, we find that sin(43°) ≈ 0.68199836. Multiplying this by 100, we get:

h ≈ 0.68199836 * 100 ≈ 68.2

Therefore, the height of the tower is approximately 68.2 feet.