2. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

3. Splash Screen

4. Example 3-2b Objective Find missing measures in 30-60 degree right triangles and 45-45 degree triangles

5. Example 3-2b Review Vocabulary Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the length of the legs a and b. C 2 = A 2 + B 2

6. Example 3-2b 30 0 – 60 0 Triangle A = ½ of C or 2A = C Remember: A is the shortest leg using the Pythagorean Theorem C 2 = A 2 + B 2 A B C

7. Example 3-2b 45 0 – 45 0 Triangle A and B are congruent A B C

8. Lesson 3 Contents Example 1Find Lengths of a 30  –60  Right Triangle Example 2Find the Lengths of a 45  Example 2Find the Lengths of a 45  –45  Right Triangle45  Right Triangle

9. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 Remember: A 30-60 triangle, the hypotenuse is twice the side opposite the 30 0 angle C = 2(6) Multiply C = 12 c = 12 in Since it is a right triangle and 2 of the 3 sides are known, use the Pythagorean Theorem c 2 = a 2 + b 2

10. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 Replace c with 12 C = 2(6) C = 12 c = 12 in c 2 = a 2 + b 2 12 2 Replace a with 6 12 2 = 6 2 12 2 = 6 2 + b 2 Bring down + b Follow Order of Operations P E MD AS Do all exponents first

11. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b 2 12 2 = 6 2 + b 2 Follow Order of Operations P E MD AS Do all exponents first 144144 = 36 Bring down + b 2 144 = 36 + b 2 Ask “What is being done to b 2 ? b 2 is being added by 36 Do the inverse on both sides of the equal sign

12. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b 2 12 2 = 6 2 + b 2 Bring down 144 144144 = 36144 = 36 + b 2 144 Subtract 36 144 - 36 Bring down = 36 144 - 36 = 36 Subtract 36 144 - 36 = 36 -36 Bring down + b 2 144 - 36 = 36 -36 + b 2 Combine “like” terms 108108 = 0 Bring down + b 2 108 = 0 + b 2

13. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in c 2 = a 2 + b 2 12 2 = 6 2 + b 2 Use the Identity Property to add 0 + b 2 144144 = 36144 = 36 + b 2 144 - 36 = 36 -36 + b 2 108108 = 0108 = 0 + b 2 108 = b 2 Ask “what is being done to the variable?” The variable is being squared Do the inverse on both sides of the equal sign

14. Example 3-1a Find each missing length. Round to the nearest hundredth if necessary. 1/2 C = 12 c = 12 in Find the square root of 108 108 = b 2 Find the square root of b 2 Combine “like” terms 10.3910.39 = b Remember: Had to solve for c and for b so need both answers with dimensional analysis Answer: b = 10.39 inches c = 12 inches

15. Example 3-1b Find each missing length. Round to the nearest hundredth if necessary. Answer: a = 10 cm, b = 17.32 cm 1/2

16. Example 3-2a BASEBALL The figure below shows the dimensions of a baseball diamond. The distance between home plate and first base is 90 feet. The area between first base, third base, and home plate forms a right triangle. Find the distance from first base to third base and the distance from third base to home plate. 2/2 Remember: A 45-45 degree triangle has congruent legs Find the right triangle area between first base, third base, and home plate forms aright triangle Since it is a right triangle, can use the Pythagorean Theorem 90 ft

17. Example 3-2a 2/2 Write the Pythagorean Theorem c 2 = a 2 + b 2 Define the variable c as the hypothesis since it is unknown cc2c2 Replace a and b with 90 since they are congruent c 2 = 90 2 + 90 2 90 ft

18. Example 3-2a 2/2 Bring down c 2 c 2 = a 2 + b 2 c2c2 c 2 = 90 2 + 90 2 c 2 = Combine “like” terms c 2 = 8,100c 2 = 8,100 + 8,100 Combine “like” terms again c 2 = 16,200 Ask “what is being done to the variable?” The variable is being squared Do the inverse on both sides of the equal sign Find the square root of c 2 c Find the square root of 16,200 c = 127.28

19. Example 3-2a 2/2 c 2 = a 2 + b 2 c2c2 c 2 = 90 2 + 90 2 c 2 = Add dimensional analysis c 2 = 8,100c 2 = 8,100 + 8,100 c 2 = 16,200 c c = 127.28c = 127.28 ft Answer: Remember: Had to solve for 2 dimensions Third to Home = 90 ft First to 3 rd = 127.28 ft Find the distance from first base to third base and the distance from third base to home plate.

20. Example 3-2b SAILING The sail of a sailboat is in the shape of a right triangle. The height of the sail is 12 feet. Find each missing length. Answer: b = 12 ft; c = 16.97 ft * 2/2

21. End of Lesson 3 Assignment Lesson 6:3Special Right Triangles3 - 16 All