6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-5

Key Concept

In any right triangle, the sum of the squares of the lengths of the legs is equal

to the square of the length of the hypotenuse. That is, if aand bare the

lengths of the legs and cis the length of the hypotenuse, then a^2 b^2 c^2.

Pythagorean Theorem

Remember:In a right

triangle, the legs are the

sides that form the right

angle. The hypotenuse is

the side oppositethe right

angle. It is the longest side

of the triangle.

hypotenuse

legs

c

b

a

c b

a

Update your skills. See page 408 III.

Pythagorean Theorem

Objective To use the Pythagorean Theorem to find a missing

side of a right triangle • To determine whether a given triangle

is a right triangle

The third-story window of a building is 12 meters above the ground.
A firefighter places the base of a ladder 9 meters from the building.
What length is necessary for the ladder to reach the window?

To solve this problem, notice that the ladder forms the hypotenuse

of a right triangle, so you can apply the Pythagorean Theorem.

You can use the Pythagorean Theorem to find the length

of the ladder.

a^2 b^2 c^2 Pythagorean Theorem

122  92 c^2 Substitute the given values 12 and 9 for aand b.

144  81 c^2 Evaluate the squares.

225 c^2 Find the sum.

 Find the positive square root of both sides.

15 c Simplify.

So the ladder must be 15 meters long in order to reach the window.

If you know the length of any two sides of a right triangle, you can

use the Pythagorean Theorem to find the length of the third side.

A television screen measures 20 inches along its diagonal and 15 inches

along its base. What is the height of the television screen to the nearest

tenth? Let a15 inches and c20 inches.

a^2 b^2 c^2 Pythagorean Theorem

152 b^2  202 Substitute the known values.

225 b^2  400 Evaluate the squares.

225  225 b^2  400  225 Subtract 225 from both sides.

b^2  175 Simplify.

 Find the positive square root of both sides.

b 13.22875656... Simplify. Use your calculator.

b13.2 Round to the nearest tenth.

So the height of the television screen is about 13.2 inches.

b^2175

225 c^2