The shorter leg of a right triangle is 8 feet less than the other leg find the length of the two legs of the hypotenuse is 40

Question

The shorter leg of a right triangle is 8 feet less than the other leg find the length of the two legs of the hypotenuse is 40

Answer 1

use the Pythagorean theorem

hypotenuse squared = sum of squares of the legs

40^2 = (s+8)^2 + s^2

2s^2 + 16s +64 = 1600

s^2 + 8s +32 = 800

s^2 +8s - 768 = 0

4 methods to solve for s (and ignore the negative solution or just change its sign and assign it to the Longer leg)

factor, complete the square, quadratic formula or graph the equation and find the positive x intercept

or use an online triangle solver

= about 24 feet

= shorter leg

add 8

= 32 feet

= longer leg

(s+32)(s-24) = when factored

set each factor = 0 and solve for s = short leg length

s = 24

add 8 to get 32 = longer leg length

or for online triangle solver

40/sin90 = 40/1 = 40 = s/sinS = (s+8)/sinL)

angle S = about 37 degrees

angle L = about 54

plug in at least 1 side and either 2 angles or another side and 1 angle, and presto chango, the online triangle solvers chews it up and spits out the other missing sides and angles