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.

Answer 1

Answer:

       $\large\boxed{ 79.1ft}$

Explanation:

The guy-wire, the highest point of the cell phone tower, and the the point on the ground that is 25 ft from the base of the tower form a right triangle, where:

• the length of the guy-wire is the hypotenuse of the triangle

• the height of the cell phone tower is one leg (75 ft)

• the distance from the point on the ground to the base of the tower is the other leg (25 ft).

Since you know the lengths of both legs, you can use Pythagora's theorem to find the hypotenuse (the lenght of the guy-wire):

$hypotenuse^2=(leg_1)^2+(leg_2)^2$

$hypotenuse^2=(75ft)^2+(25ft)^2$

$hypotenuse^2=5,625ft^2+625ft^2=6,250ft^2$

$hypotenuse=\sqrt{6,250ft^2}\approx 79.06ft\approx 79.1ft$