1. Aim: How do we find the lengths of the sides in a right triangle? Do Now 1. Solve 2(x + 5) = -14 2. Find the measure of the missing angle? 48 o 17 o 100 o 3. Find the surface area and the volume of a cylinder with a radius of 5 inches and a height of 9 inches. Leave your answers in terms of pi.

2. Aim: How do we find the lengths of the sides in a right triangle? hypotenuse leg Pythagorean Theorem For any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a c b = 3 = 5 = 4 a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 leg 2 + leg 2 = hypotenuse 2 9 + 16 = 25 25=25 In a right triangle, ·the side opposite the right angle, is the hypotenuse ·the sides that form the right angle are called legs

3. Aim: How do we find the lengths of the sides in a right triangle? hypotenuse leg a c b = 12 = ? = 9 1. Find the length of the hypotenuse of a right triangle with a 12 inch leg and a 9 inch leg. 12 2 + 9 2 = c 2 a 2 + b 2 = c 2 leg 2 + leg 2 = hypotenuse 2 144 + 81 = c 2 15 = c hypotenuse = 15 inches 225 = c 2

4. Aim: How do we find the lengths of the sides in a right triangle? hypotenuse leg a c b = 6 = ? = 8 2. Find the length of the hypotenuse of a right triangle with a 6 foot leg and an 8 foot leg. 6 2 + 8 2 = c 2 a 2 + b 2 = c 2 leg 2 + leg 2 = hypotenuse 2 36 + 64 = c 2 100 = c 2 10 = c hypotenuse = 10 feet

5. Aim: How do we find the lengths of the sides in a right triangle? 3. Find the length of the hypotenuse of a right triangle with a 8 foot leg and an 15 foot leg. 4. Find the length of the hypotenuse of a right triangle with a 12 foot leg and a 16 foot leg. 8 2 + 15 2 = c 2 a 2 + b 2 = c 2 leg 2 + leg 2 = hypotenuse 2 64 + 225 = c 2 17 = c 144 + 256= c 2 12 2 + 16 2 = c 2 leg 2 + leg 2 = hypotenuse 2 400= c 2 20 = c 289= c 2 a 2 + b 2 = c 2 17 feet 20 feet

6. Aim: How do we find the lengths of the sides in a right triangle? hypotenuse leg a c b = 7 = 11 = ? 5. A right triangle has a hypotenuse length of 11 inches and a leg length of 7 inches. What is the length of the other leg. Round your answer to the nearest tenth. 7 2 + b 2 = 11 2 a 2 + b 2 = c 2 leg 2 + leg 2 = hypotenuse 2 49 + b 2 = 121 b 2 = 72 leg ≈ 8.5 inches b ≈ 8.5 -49

7. Aim: How do we find the lengths of the sides in a right triangle? For each right triangle, find the length of the missing side. Round your answer to the nearest tenth, if necessary. 12 5 6) 2 6 7)

8. Aim: How do we find the lengths of the sides in a right triangle? 23 miles 16 miles 8) How far is Little Red Riding Hood from my mansion? Round your answer to the nearest tenth of a mile?

9. Aim: How do we find the lengths of the sides in a right triangle? Jackson 5 yd 4 yd Westbrook Mcnabb 9) How far will Westbrook have to throw the ball to Mcnabb.

10. Aim: How do we find the lengths of the sides in a right triangle? 17 miles 53 miles 10) How far is the Big Bad Wolf from the little pig? Round your answer to the nearest mile.

11. Aim: How do we find the lengths of the sides in a right triangle? 11) The size of a TV is measured by its diagonal. How big is this TV? 36 inches 48 inches

12. Aim: How do we find the lengths of the sides in a right triangle? 12) A ladder is leaning against a building. The base of the ladder is 8 feet from the building. The top of the ladder reaches 6 feet from the ground. How long is the ladder? 13) A 15 foot wire is stretched from the top of 7 foot utility pole to a stake in the ground. How far is the bottom of pole from the stake? Round your answer to the nearest tenth.

13. Aim: How do we find the lengths of the sides in a right triangle? 14) An apartment window is 21 feet above the ground. The top of a 35-foot ladder is resting on the window sill. How far is the bottom of the ladder from the base of the building ? 15) A 34 foot ladder is leaning against a building. The bottom of the ladder is 30 feet from the base of the building. How far up does the ladder meet the wall? Round your answer to the nearest tenth?

14. Aim: How do we find the lengths of the sides in a right triangle? 16) A wire with a length of 25 meters is attached to a utility pole. The wire is anchored to the ground 20 meters from the base of the pole. How long is the pole? 17) A rope is attached from the top of a 8 foot pole to a stake in the ground. The stake is 4 feet from the pole. How long is the rope? Round your answer to the nearest tenth.

15. Aim: How do we find the lengths of the sides in a right triangle? 15 20 25 Converse of the Pythagorean Theorem – If a 2 +b 2 =c 2, then the triangle is a right triangle. a 2 +b 2 =c 2 Determine whether the triangles are right triangles. 10 12 16 18) 19) 15 2 +20 2 =25 2 225+400=625 625=625 a 2 +b 2 =c 2 10 2 +12 2 =16 2 100+144=256 244≠256 This is a right triangle.This is not a right triangle. **Hypotenuse is always the longest side.

16. Aim: How do we find the lengths of the sides in a right triangle? 14 17 23 Determine whether a triangle with the given side lengths is a right triangle. a = 22, b = 120, c = 122 20) 21)

17. Aim: How do we find the lengths of the sides in a right triangle? (2009)

18. Aim: How do we find the lengths of the sides in a right triangle? (2009)

19. Aim: How do we find the lengths of the sides in a right triangle? (2007)

20. Aim: How do we find the lengths of the sides in a right triangle? (2008)

21. Aim: How do we find the lengths of the sides in a right triangle? (2008)

22. Aim: How do we find the lengths of the sides in a right triangle? (2007)

23. Aim: How do we find the lengths of the sides in a right triangle? (2007)