Question

A guy-wire extends from the top of a cell phone tower to a point on the
ground that is 25 ft from the base of the tower.
What is the approximate length of the guy-wire if the height of the cell
phone tower is 75 ft?
Round your answer to the nearest tenth.

70.7 ft
79.1 ft
10.0 ft
7.1 ft

Answer 1

Answer:

79.1 ft

Step-by-step explanation:

Draw a vertical segment about 3 inches tall. Label the upper endpoint A and the lower endpoint B. That is the cell phone tower. Starting at point B, draw a horizontal segment 1 inch long to the right. Label the right endpoint C. Connect C to A with a segment.

Segment BC is 25 ft long. Segment AB is 75 ft long. Angle B is a right angle.

You are looking for the length of segment AC, the guy wire length.

Triangle ABC is a right triangle with right angle B.

Sides AB and BC are the legs, and side AC is the hypotenuse.

We can use the Pythagorean Theorem:

(leg1)^2 + (leg2)^2 = (hyp)^2

Let one leg be a, the other leg be b, and let the hypotenuse be c.

Then you have

a^2 + b^2 = c^2

We have a = 75 ft

b = 25 ft

We are looking for c, the length of the hypotenuse.

(75 ft)^2 + (25 ft)^2 = c^2

5625 ft^2 + 625 ft^2 = c^2

6250 ft^2 = c^2

c^2 = 6250 ft^2

Take the square root of both sides.

c = 79.0569... ft

Answer: 79.1 ft

Answer 2

The answer is 79.1 ft.