1. Extra Practice for Sem 2, Quiz 5

2. 21√3 60  21 42 30  I have the short leg, so to get  long leg, multiply by √3  hyp, multiply by 2 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

3. 21 45  21 21√2 45  I have a leg, so the other leg is congruent, and to get the hyp, multiply by √2 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

4. 9√3 30  18 9 60  I have the hyp, so get short leg first by dividing by 2 Then, from the short leg to get the long leg, multiply by √3 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

5. 17√3 2 30  17 2 60  I have the hyp, so get short leg first by dividing by 2 Then, from the short leg to get the long leg, multiply by √3 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

6. 7√6 60  14√2 7√2 30  I have the hyp, so get short leg first by dividing by 2 Then, from the short leg to get the long leg, multiply by √3 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

7. 36 60  24√3 12√3 30  I have the hyp, so get short leg first by dividing by 2 Then, from the short leg to get the long leg, multiply by √3 12√3√3 = 123 = 36 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

8. 48 60  24√3 24 30  I have the long leg, so get short leg first by dividing by √3 Then, from the short leg to get the hyp, multiply by 2 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

9. 20√2 60  10√6 10√2 30  I have the long leg, so get short leg first by dividing by √3 Then, from the short leg to get the hyp, multiply by 2 10√6 √3 √2 = 10√2 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

10. 12√3 60  18 6√3 30  I have the long leg, so get short leg first by dividing by √3 Then, from the short leg to get the hyp, multiply by 2 √3 = 18√3 3 18 √3 = 6√3 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

11. 40√3 3 30  20 20√3 3 60  I have the long leg, so get short leg first by dividing by √3 Then, from the short leg to get the hyp, multiply by 2 √3 = 20√3 3 20 √3 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

12. 12√5 45  12√10 12√5 45  I have the hyp, so to get the legs, divide by √2 12√10 √2 √5 = 12√5 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

13. √2 = 42√2 2 21√2 42 21√2 45  I have the hyp, so to get the legs, divide by √2 42 √2 = 21√2 45  Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form

14. √2 = 5√14 2 Answers in simplified radical form Use special right ∆ rules to solve the triangle. Answers in simplified radical form 5√7 5√14 2 45  I have the hyp, so to get the legs, divide by √2 5√7 √2 5√14 2 45 

15. 23 I have the hyp and the side adj to A, so I will use the cos. cosA = 16/23 A = cos -1 (16/23) A = 45.9  16 A B C 45.9  Round to the nearest tenth. Use Soh Cah Toa, or the Pythagorean Thm, to solve the triangle. Round to the nearest tenth.

16. 23 I have the hyp and the side opp to B, so I will use the sin. sinA = 16/23 A = sin -1 (16/23) A = 44.1  16 A B C 45.9  44.1  Check: 44.1 + 45.9 = 90 yes! Round to the nearest tenth. Use Soh Cah Toa, or the Pythagorean Thm, to solve the triangle. Round to the nearest tenth.

17. 23 I have several choices for finding the missing side. I am using the sin of A; I’m looking for adj side, and I have the hyp. sin (45.9) = x 1 23 x = 23sin(45.9) x = 16.5 16.5 16 A B C 45.9  44.1  Check: 16.5 2 + 16 2 = 23 2 528.25 ≈ 529

18. 50 I have the side opp of A, so I will use the sin to find the hyp. A B C 21  Round to the nearest tenth. Use Soh Cah Toa, or the Pythagorean Thm, to solve the triangle. Round to the nearest tenth. sin (21) = 50 1 x x sin (21) = 50 x = 50 sin (21) x = 139.5 139.5

19. 50 I have the side opp of A, so I will use the tan to find the adj side. A B C 21  Round to the nearest tenth. Use Soh Cah Toa, or the Pythagorean Thm, to solve the triangle. Round to the nearest tenth. tan (21) = 50 1 x x tan (21) = 50 x = 50 tan (21) x = 130.3 139.5 130.3 Check: 50 2 + 130.3 2 = 139.5 2 19452.04 ≈ 19460.25

20. 50 A B C 21  Round to the nearest tenth. Use Soh Cah Toa, or the Pythagorean Thm, to solve the triangle. Round to the nearest tenth.  B = 90 – 21 = 69 139.5 130.3 Check: sin(69) = 130.3 / 139.5.9336 ≈.9341 69 