MTH 092

Section 15.6The Pythagorean Theorem

Right Triangles

• A right triangle is a triangle that has one right (90-degree) angle.

• The side opposite the right angle is called the hypotenuse. The other two sides are called legs.

• In a right triangle, the hypotenuse will always be the longest side.

Here’s A Picture

The Pythagorean Theorem

• Only applies to right triangles.• Is used to find missing lengths.• Reads as follows: in a right triangle, the sum of

the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In Other Words…

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Exact Answers and Decimal Approximations

• An exact answer means that you do not approximate the radical by using a calculator.

• A decimal approximation means that you use a scientific (or other) calculator to “find” the square root.

• For example:• is an exact answer.• 4.795831523… is a decimal approximation.

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Examples

Use the Pythagorean Theorem to find the unknown side of each right triangle. Give an exact answer and a two-decimal place approximation.1.a = 2, b = 32.a = 3, b = 63.a = 7, b = 244.a = 4, c = 135.b = 2, c = 6

More Examples6. A wire is used to anchor a 20-foot-tall pole. One end

of the wire is attached to the top of the pole. The other end is fastened to a stake five feet away from the bottom of the pole. Find the length of the wire rounded to the nearest tenth of a foot.

7. Elizabeth Kaster is flying a kite. She let out 80 feet of string and attached the string to a stake in the ground. The kite is now directly above her brother Mike, who is 32 feet away from the stake. Find the height of the kite to the nearest foot.