Question

Patty sits on a bench with her laptop 2,456 feet from the base of the WiFi antenna and the angle of elevation from her laptop, which is 2.5 feet from the ground, to the top of the antenna is 58 degrees. How tall is the antenna?

Answer 1

Explanation:

Let's call the height of the antenna "h". We can use the tangent function to find "h" since we have the opposite (the height from the laptop to the top of the antenna) and the adjacent (the distance from Patty to the base of the antenna) sides of the right triangle.

The tangent of the angle of elevation (58 degrees) is equal to the opposite (h - 2.5 feet) divided by the adjacent (2,456 feet):

tan(58) = (h - 2.5) / 2456

We can solve for "h" by multiplying both sides by 2456 and adding 2.5:

tan(58) * 2456 + 2.5 = h

Using a calculator, we get:

h ≈ 3,929.1 feet

Therefore, the antenna is approximately 3,929.1 feet tall.