The Pythagorean Theorem

Parts of a
Right
Triangle

•In a right triangle, the two sides adjacent to
the right angle are known as the legs , or
a and b .

•The side opposite from the right angle
is called the hypotenuse , or c .

•The hypotenuse is always the longest side of a right
triangle.

Pythagorean
Theorem

•The Pythagorean theorem tells us how the side lengths
of right triangles are related.

•In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This
relationship can be represented by the equation:

a² + b² = c²

Label a, b, and c on each of the right triangles below.

Finding side lengths of right
triangles

• Label a , b , and c .

• Substitute the known values into the Pythagorean theorem.

• Solve for the missing variable.

Use the steps below to find the missing side length of the right triangle in example 1.

Find the missing side length of each right triangle. Round to the nearest tenth if necessary.

Use the Pythagorean theorem to find the missing side length
in each right triangle. Round to the nearest tenth if necessary.

Apply the Pythagorean theorem to answer 7-8. Round to the
nearest tenth if necessary.

7. A rectangular pool at Andy’s gym
measures 25 meters by 50 meters. How
many meters would Andy need to swim in
order to swim diagonally across the pool?

8. A pole vaulter rests a 17-foot pole
against a wall. If the top of the pole hits the
wall 14 feet above the ground, how far
from the wall is the bottom of the pole?