Question

A wire is attached to the top of a telephone pole. The wire is 16 ft long. The wire makes a 30-degree angle with the ground. How tall is the telephone pole?

Answer 1

To find the height of the telephone pole, use the cosine of the angle which is 30 degrees. The height is found to be 8√3 ft, which is approximately 13.86 ft tall.

Step-by-step explanation:

The student has asked to find the height of a telephone pole when a wire is attached to its top and makes a 30-degree angle with the ground. To solve this, we can use trigonometric ratios. Specifically, we use the cosine function for this calculation since the wire makes an angle with the ground, and we are looking for the adjacent side to the angle, which is the height of the pole.

Let's denote the height of the telephone pole as 'h'. Using the cosine function, we have:

cos(30°) = h/16 ft

As the cosine of 30° is equal to √3/2, the equation can be written as:

(√3/2) = h/16 ft

By multiplying both sides by 16 ft, we find the height (h) of the telephone pole:

h = 16 ft × (√3/2)

h = 8√3 ft

The telephone pole is 8√3 ft tall, which is approximately 13.86 ft.