The shorter leg of a right triangle is 21 feet less than the other leg. Find the length of the two legs if the hypotenuse is 39 feet.

leg 1 = 36 feet

leg2 = 15 feet

Step-by-step explanation:

Hi, we have to apply the Pythagorean Theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse of the triangle (in this case the distance between Doreen's house and the tower) and a and b are the other legs.

leg1 = x

leg2 = x-21 (21 feet less than the other leg)

Replacing with the values given:

39^2 = x^2 + (x-21) ^2

1,521 = x^2 + x^2 - 42x + 441

0 = 2x^2 - 42x + 441-1,521

0 = 2x^2 - 42x - 1,080

For: ax2 + bx + c

x = [ - b ± √b²-4ac] / 2a (quadratic formula)

Replacing with the values given:

x = - (-42) ± √ (-42) ²-4 (2) - 1080] / 2 (2)

x = 42± √10,404] / 4

x = 42± 102 / 4

Positive:

x = 42+102 / 4 = 36

leg 1 = 36

leg2 = 36-21 = 15

Feel free to ask for more if needed or if you did not understand something.