Question

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if c=9 and a=7

Answer 1

b = 5.65

Explanation:

Since it's a right triangle, we can apply the Pythagorean theorem.

We know that the hypotenuse is 9, and one leg is 7. We are missing the other leg which is called b.

The Pythagorean theorem tells us that if the hypotenuse is c and the legs of the right triangle are a and b, then we have
`c^(2) = a^(2) +b^(2)`

So we're going to solve this formula for the values given c= 9 and a = 7

`9^(2) =7^(2) +b^(2) \\81=49+b^(2) \\81-49=b^(2) \\32=b^(2) \\√(32) =b`

Thus, b =
`√(32) =5.65`

Answer 2

Apply the Pythagoras Theorem


`{c }^(2) = {a}^(2) + {b}^(2)`

`{9 }^(2) = {7}^(2) + {b}^(2)`

`81 = 49+ {b}^(2)`

`81 - 49 = {b}^(2)`

`32= {b}^(2)`
Take square root of both sides


`b = √(32)`

`b = 4 √(2)`