Because the given triangle contains a right angle (90°), we can use the Pythagorean Theorem.
Pythagorean Theorem:
a²+b²=c²
where a=leg 1, b=leg 2, and c=hypotenuse
The Pythagorean Theorem works to solve any side of a right triangle as long as we know t he length of 2 sides. So, let’s plug the values into the formula and solve for “a” (leg 1).
a²+(4)²=(4√5)²
Simplify:
a²+16=80
Solve for a:
Subtract 16 from both sides
a²=80-16
a²=64
Take the positive square root of both sides:
√a²=√64
a=8
So, leg 1 (a), or side 3 is equal to 8
Let’s check our work by plugging a=8 because into the formula:
(8)²+16=80
64+16=80
80=80
Thus, the 3rd side is 8