Question

A cable extends from the top of a radio tower to a point 360 feet from the base of the tower. If the

cable is 850 feet long, how tall is the tower?

Answer 1

770 feet

Explanation:

Given

• Cable = 850 feet long
• Extends from radio tower to a point 360 feet from the base of a tower

Solving

• Using the Pythagorean Theorem, we can find the height
• (distance from base)² + (height)² = (length of cable)²
• height² = (850)² - (360)²
• height² = 722,500 - 129,600
• height² = 592,900
• height = √592,900
• height = 770 feet

Answer 2

Explanation:

we have a right-angled triangle :

the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.

then the ground distance (360 ft) and the height of the tower are the 2 legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

in our case

850² = 360² + height²

height² = 850² - 360² = 592,900

height = 770 ft

the tower is 770 ft tall.