Two poles, A and B, are 12 meters apart. Pole A is 5 meters high. A rope 20 meters long is tied to the top of pole A and stretches to the top of pole B. What is the height of pole B? Assume that pole B is taller than pole A.

Let the height of pole B be x meters.

We have a right angled triangle whose base = 12 m, hypotenuse = 20 m and height = (x - 5) m.

Applying the pythagoras theorem:-

20^2 = (x - 5) ^2 + 12^2

x^2 - 10x + 25 = 20^2 - 12^2

x^2 - 10x + 25 = 256

x^2 - 10x - 231 = 0

(x - 21) (x + 11) = 0

x = 21, - 11 We ignore the negative root

So the Pole B is 21 meters high. Answer