1. Warm UP

2. Essential Question How can I solve for side lengths of a right triangle and how can you use side lengths to determine whether a triangle is acute, right, or obtuse?

3. Lesson 41 Unit 2: Right Triangles Section 1: The Pythagorean Theorem

4. Standard(s): MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

5. Pythagorean theorem - The theorem states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the hypotenuse.

6. NOTE: The hypotenuse is always directly across from the 90 degree angle

7. We can use the Pythagorean theorem to solve for a missing side length in right triangles Find the missing variable: 1.A = 6, B= 9, C = ? 2.A = 4, B = ? C = 11 3.A = ? B = 4, C = 13 4.A = 2, B = 13, C = ? 5.A =7, B = ? C = 14 A B C

8. Application Problem To prevent a ladder from shifting, safety experts recommend that the ratio of h:d be 4:1. How far from the base of the wall should you place the foot of a 10- foot ladder? Round to the nearest inch.

9. Solution Based on the picture and what we know about The Pythagorean theorem: D 2 + h 2 = l 2 We also know l = 10 because the Ladder is 10 feet tall Let d have length x. Based on the ratio, h = 4x So, (x) 2 + (4x) 2 = (10) 2

10. Pythagorean triple A set of 3 nonzero whole numbers a, b, and c such that a 2 + b 2 = c 2. - The largest side length is the hypotenuse Some common Pythagorean triples are: 3,4,5 5,12,13 8,15,17 7,24,25

11. Find the missing side length and Identify if the following is a Pythagorean triple 15 12

12. Find the missing side length and Identify if the following is a Pythagorean triple 15 9

13. In order to have a triangle The two smaller side lengths added together must be larger than the largest side length If they aren’t the sides can’t touch 17 1 7 15 8

14. Different kinds of triangles Right triangles angle C = 90 degrees c 2 = a 2 + b 2 Obtuse triangles Angle C > 90 degrees c 2 > a 2 + b 2 Acute triangles angle C < 90 degrees c 2 < a 2 + b 2 Note: c is the longest side of the triangle

15. Tell if the measures can be the side lengths of a triangle. If so, Classify the triangle as acute, obtuse, or right a.8,11,13 b.5.8, 9.3, 15.6