1. Find the hypotenuse in a right triangle with legs a = 3 and b = 4. 55 Exercise

2. Find the hypotenuse in a right triangle with legs a = 3 and b = 3. 3 √ 23 √ 23 √ 23 √ 2

3. Find the missing side length in a right triangle with leg b = 4 and hypotenuse 4 √ 2. 44 Exercise

4. Find the hypotenuse in a right triangle with legs a = 3 and b = 3 √ 3. 66 Exercise

5. Find the missing side length in a right triangle with leg b = 5 √ 3 and hypotenuse 10. 55 Exercise

6. AA CCBB

7. 45° 11 cc 11

8. a1a1 a1a1 c√ 2c√ 2 c√ 2c√ 2 ==

9. 45-45 Right Triangle If each leg of a 45-45 right triangle is a units long, then the hypotenuse is a √ 2 units long. 45° aa a √ 2a √ 2a √ 2a √ 2 aa

10. Find the length of the hypotenuse in the 45-45 right triangle. 45° 33 xx 33 3 √ 23 √ 23 √ 23 √ 2 Example 1

11. Find the length of the legs in the 45-45 right triangle. 45° aa aa 5 √ 25 √ 25 √ 25 √ 2 55 Example 2

12. If a = 2, what is c? 45° aa cc bb 2 √ 22 √ 22 √ 22 √ 2 Example

13. If c = 8, what is a? 45° aa cc bb 4 √ 24 √ 24 √ 24 √ 2 Example

14. If the perimeter is 6 + 6 √ 2, what are a and c? 45° aa cc bb a = 3 √ 2 and c = 6 Example

15. If the perimeter is 20, what is a? 45° aa cc bb ≈ 5.86 Example

16. Are 5, 5, and 7 the sides of a 45-45 right triangle? no Example

17. 60° 30°

18. 30-60 Right Triangle If the short leg of a 30-60 right triangle is a units long, then the long leg is a √ 3 units long and the hypotenuse is 2a units long. 60° 2a2a2a2a a √ 3a √ 3a √ 3a √ 3 30° aa

19. Find the missing lengths x and y in the triangle. 60° 44 xx 30° yy Since a = 4, the long leg is 4 √ 3 and the hypotenuse is 2(4) = 8 units. Example 3

20. Find the short leg and hypotenuse of a 30-60 right Δ whose long leg is 6 √ 3. Since the long leg of a 30-60 right triangle is a √ 3 = 6 √ 3, it follows that the short leg it a = 6. Then the hypotenuse is 2a = 2(6) = 12. Example 4

21. Find the long leg and short leg of a 30-60 right triangle whose hypotenuse is 9. The hypotenuse is 2a = 9, so the short leg is a = 4.5. The long leg is a √ 3 = 4.5 √ 3. Example 5

22. If a = 1, what are b and c? 60° aa cc 30° bb b = √ 3 and c = 2 Example

23. If c = 7, what is a? 60° aa cc 30° bb 7272 7272 = 3.5 Example

24. If a = 3, what is the perimeter? 60° aa cc 30° bb 9 + 3 √ 3 ≈ 14.2 Example

25. If the perimeter is 25, what is c? 60° aa cc 30° bb 10.566 Example

26. We know that 3, 4, and 5 are the lengths of the sides of a right triangle. Are they the sides of a 30-60 right triangle? no; 5 ≠ 2(3) Example

27. Find the other two sides in a 30-60 right triangle with a short leg of √ 5. long leg: √ 15; hypotenuse: 2 √ 5 sides: 2.2, 3.9, 4.5 Exercise

28. Find the other two sides in a 30-60 right triangle with a short leg of 2 √ 7. long leg: 2 √ 21; hypotenuse: 4 √ 7 sides: 5.3, 9.2, 10.6 Exercise

29. Find the other two sides in a 30-60 right triangle with a long leg of 20 √ 3. short leg: 20; hypotenuse: 40 sides: 20, 34.6, 40 Exercise