Math question’s

Question

a telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 21 feet less than the height of the pole. If the wire is to be 3 feet longer than the height of the pole, what is the height of the pole

Answer 1

p = 21+ b

w=3 +p= 3+21+b = 24 +b

it's a right triangle with sides p and b, with hypotenuse = w = wire length

(24+b)^2 = b^2 + (21+b)^2

b^2 + 48b + 576 = b^2 + b^2 + 42b + 441

b^2 -6b -135 = 0

b^2 -6b + 9 = 135 +9 = 144

b-3 = 12

b = 15, b+24 = 39, b+21 = 36

wire = 39, pole = 36 feet