SOLUTION: #1---The length of one leg of a right triangle is 12 meters. the length of the hypotenuse is 8 meters longer than the other leg. find the length of the hypotenuse and the other leg

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Question 331134: #1---The length of one leg of a right triangle is 12 meters. the length of the hypotenuse is 8 meters longer than the other leg. find the length of the hypotenuse and the other leg of the triangle.

#2---Two angles are supplementary if the sum of their angles is 180 degrees. One of two supplementary angles is 8 degrees less than three times the other. find the measure of each angle.
Answer by mananth(16946) (Show Source):
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#1---The length of one leg of a right triangle is 12 meters. the length of the hypotenuse is 8 meters longer than the other leg. find the length of the hypotenuse and the other leg of the triangle.
let the other leg be x
one leg = 12
hyp = x+8
(x+8)^2=x^2+12^2
x^2+16x+64=x^2+144
16x+64=144
add -64
16x+64-64=144-64
16x=80
x= 5 the other leg.
Hypotenuse = x+8 = 5+8=13

#2---Two angles are supplementary if the sum of their angles is 180 degrees. One of two supplementary angles is 8 degrees less than three times the other. find the measure of each angle.
let one angle be x
the other angle = 3x-8
..
3x-8+x=180
4x-8=180
add 8
4x-8+8=180+8
4x=188
divide by 4
4x/4=188/4
x=47 one angle
second angle = 180 -47=133