Determine the length of the missing side of each right triangle. Show your work.

Question

1)a=15; b=?; c=20
Answer is b= 5√7

2)a=9; b=12; c=?
Answer is c= 15

**How do I show my work to come up with each of these two answers?
THANK YOU!!

Answer 1

1. a^2 + b^2 = c^2.
15^2 + b^2 = 20^2,
225 + b^2 = 400.
b^2 = 400-225 = 175,
b = sqrt(25*7) = 5*sqrt7.

2. 9^2 + 12^2 = c^2.
c^2 = 81 + 144 = 225,
c = sqrt(225) = 15.

Answer 2

1)

b = √ ( c ^ 2 - a ^ 2 )

b = √ ( 20 ^ 2 - 15 ^ 2 )

b = √ ( 400 - 225 )

b = √ ( 175 )

b = √ ( 7 * 25 )

b = √ 7 * √ ( 25 )

b = √ 7 * 5

2)

c = √ ( a ^ 2 + b ^ 2 )

c = √ ( 9 ^ 2 + 12 ^ 2 )

c = √ ( 81 + 144 )

c = √ ( 225 )

c = 25