7.2 Find the Length of the Hypotenuse

Common Core Standards 8. EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. 8. G.6 Explain a proof of the Pythagorean Theorem and its converse. 8. G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions WARM-UP 1) Only copy the right triangle.

57o

116o 38o 85o

Copy the right triangles and circle the length of the hypotenuse.

2) 5 3) 13 3 5 12 4 Find the Length of the Hypotenuse

If you know the lengths of two sides of a right triangle can you always figure out the length of the other side?

? 3

4 NOTES The two short sides of a right triangle are called the legs. The longest side is called the hypotenuse. Examples Identify the hypotenuse and the legs of the right triangles. E A J K

B C D F L NOTES The Pythagorean Theorem: The sum of the squares of the two legs of a right triangle always equals the square of the hypotenuse. leg22+= leg hyp 2

Examples Find the length of the hypotenuse.

4 NOTES Lengths can never be negative so we discard the negative solution of the quadratic equation because it makes no sense.

Examples Find the length of the hypotenuse.

12 NOTES The hypotenuse must be the longest side.

Examples Eliminate the answers that are not possible values for the hypotenuse. Find the length of the 10 hypotenuse.

24 a) 8 b) 15 c) 25 d)26 EXAMPLES Find the length of the hypotenuse. EXAMPLES Find the length of the FC.

E F A 8 cm H 6 cm D C PRACTICE A ladder leans against a wall. The top of the ladder is 8 feet from the ground. The bottom of the ladder is 6 feet from the wall. How long is the ladder?

12 ft

9 ft PRACTICE Find the length of the hypotenuse of a right triangle if the two legs are 15 inches and 20 inches. FINAL QUESTION Find the length of the GD.

E F A B

H G 5 cm D 12 cm PRACTICE Find the length of the hypotenuse. Round your answer to the nearest tenth.

8 NOTES There are very few right triangles in which all three sides have whole number lengths.

Example Find the length of the hypotenuse. Round your answer to the nearest whole number.