Question

How do I find the sides of a right triangle given a=5 and hyp=10?

Answer 1

The third side has a length of `5sqrt(3)`

Explanation:

By the Pythagorean Theorem
`color(white)("XXX")a^2+b^2 = c^2` where `a, b, c` are the sides of a right triangle, with `c` the hypotenuse.

Therefore, using the given values:
`color(white)("XXX")5^2 + b^2 = 10^2`

`color(white)("XXX")rarr b^2= 75`

`color(white)("XXX")rarr b = sqrt(75) = sqrt(5^2*3) = 5sqrt(3)`