the height of a wind power

Question

need help!!

the height of a wind power assessment tower is 5m shoter than the guy wire that supports it. if the guy wire is anchored 15m from the foot of the antenna, how tall is the antenna?

Answer 1

Let X = length of the wire

Then X - 5 = height of tower 

 

It sounds like the wire, the tower, and the distance from the tower to the wire anchor form a right triangle with the wire as the hypotenuse, in which case the Pythagorean Theorem implies 

 

(X-5)² + 15² = X²

X² - 10X + 25 + 225 = X²

-10X + 250 = 0

-10X = -250

X = 25  is the length of the wire

 

So X - 5 = 20m is the height of the tower

 

Check:  15² + 20² = 225 + 400 = 625 = 25²