# Lesson 8

Finding Unknown Side Lengths

### Lesson Narrative

The purpose of this lesson is to use the Pythagorean Theorem to find unknown side lengths of a right triangle.

### Learning Goals

Teacher Facing

• Calculate unknown side lengths of a right triangle by using the Pythagorean Theorem, and explain (orally) the solution method.
• Label the “legs” and “hypotenuse” on a diagram of a right triangle.

### Student Facing

Let’s find missing side lengths of right triangles.

### Student Facing

• If I know the lengths of two sides, I can find the length of the third side in a right triangle.
• When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.

Building Towards

### Glossary Entries

• Pythagorean Theorem

The Pythagorean Theorem describes the relationship between the side lengths of right triangles.

The diagram shows a right triangle with squares built on each side.  If we add the areas of the two small squares, we get the area of the larger square.

The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as $$a^2+b^2=c^2$$.

• hypotenuse

The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.

Here are some right triangles. Each hypotenuse is labeled.

• legs

The legs of a right triangle are the sides that make the right angle.

Here are some right triangles. Each leg is labeled.