How long is the hypotenuse of the following triangle? Round your answer to the nearest tenth.

We know how long the legs are, which means we know a and b. All we've gotta do is plug both those dudes into the Pythagorean Theorem and solve for c.

a² + b² = c²

(5.1)² + (3.7)² = c²

c ≈ 6.3

Solve for b in the following right triangle. Round your answer to the nearest tenth.

This time, we know the hypotenuse and one of the legs. So let's rearrange ol' Pythagoras to find the other leg, b.

a² + b² = c²

b² = c² – a²

Plug in a = 12.0 and c = 15.0. Remember, side c always, always needs to be the hypotenuse, a.k.a. the side opposite the right angle, a.k.a. the triangle's longest side. If we mix up a leg and the hypotenuse, we'll be up a creek.

b² = (15.0)² – (12.0)²

b = 9.0

How long is side a? Round your answer to the nearest tenth.

We're after one of the legs, so slide a couple things around in the Pythagorean Theorem to solve for a.

a² + b² = c²

a² = c² – b²

Now plug in what we know. Plug like the wind!

a² = (32.7)² – (24.2)²

a = √(32.7² – 24.2²)

a ≈ 22.0