1. Extra Practice for Sem 2, Quiz 6

2. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
I have the short leg, so to get
long leg, multiply by √3 x
30
5√3
60 5

3. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
I have a leg, so to get the hyp, multiply by √2
45 x
16√2
45 16

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

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

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

7. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
6√3
I have the hyp, so get short leg first by dividing by 2
60
Then, from the short leg to get the long leg, multiply by √3 18 x
12√3
30
6√3•√3 = 6•3 = 18

8. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
I have the long leg, so get short leg first by dividing by √3 48
60
Then, from the short leg to get the hyp, multiply by 2
48√3 96 x
30

9. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
I have the long leg, so get short leg first by dividing by √3
8√2
60
Then, from the short leg to get the hyp, multiply by 2
8√6
16√2
30 √2
8√6 √3
= 8√2

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

11. Use special right ∆ rules to find the exact value of x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
I have the hyp, so to get the legs, divide by √2
45
4√6 x
4√3 √3
4√6 √2
= 4√3
45

12. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.33
cos(x) = 27/33
x = cos-1 (27/33)
x = 35.1 x 27

13. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
sin (20) = 80 x
x =
sin (20)
x = 233.9 x 80
20

14. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
tan (29) = x
x = 17tan (29)
x = 9.4
29 17 x

15. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
cos(x) = 97/133
x = cos-1 (97/133)
x = 43.2 x
133 97

16. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
sin (65) = x
x = 41sin (65)
x = 37.2 41
65 x

17. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
tan(x) = 24/10
x = tan-1 (24/10)
x = 67.4 x 10 24

18. Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
cos(72) = 18 x
x =
cos(72)
x = 58.2
72 x 18

19. Use Pythagorean Thm to find the value of x. Round to the nearest tenth.18 24

20. Use Pythagorean Thm to find the value of x. Round to the nearest tenth.50 x 48

21. Use Pythagorean Thm to find the value of x. Round to the nearest tenth.20 x 12

22. Use Altitude-on-hypotenuse theorems to find the value of x
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x =
10x = 25
x = 2.5 5 x 10

23. Use Altitude-on-hypotenuse theorems to find the value of x
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x =
5x = 9
x = 1.8 3 x 5

24. Use Altitude-on-hypotenuse theorems to find the value of x
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x =
x + 12
x2 + 12x = 64
x2 + 12x – 64 = 0
(x – 4)(x + 16) = 0
x = x = -16 x 8 12

25. x 6 5 x = 6 6 x + 5 x2 + 5x = 36 x2 + 5x – 36 = 0 (x – 4)(x + 9) = 0
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x =
x + 5
x2 + 5x = 36
x2 + 5x – 36 = 0
(x – 4)(x + 9) = 0
x = x = -9 x 6 5

26. Use Altitude-on-hypotenuse theorems to find the value of x
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
= x2
x2 =
x2 = 225
x = 15 9 x 12

27. Factor.
x2 + 12x + 32
(x + 4)(x + 8)

28. Factor
x2 – 12x + 32
(x – 4)(x – 8)

29. Factor
x2 – 4x + 32
(x + 4)(x – 8)

30. Factor
x2 + 14x + 45
(x + 9)(x + 5)

31. Factor
x2 + 15x + 36
(x + 12)(x + 3)

32. I am standing on the ground looking up at the top of a building at an angle of elevation of 75˚. If I am currently 40’ from the door, how tall is the building?
tan (75) = x
x = 40tan (75)
x = 149.3’ x 40
75˚

33. I am standing at the top of a building, looking at an ice cream truck at an angle of depression of 48˚. If the distance from me to the ice cream truck is 64yds, how far is the ice cream truck from the building?
cos (48) = x
x = 64cos(48)
x = 42.8yds x 64
48˚

34. I am looking down into the ocean, and I see a shark exactly 20 feet from me. If the shark is 15 feet below the surface of the water, what is the angle of depression at which I see him?
sin(x) = 15/20
x = sin-1 (15/20)
x = 48.6 20 15 x˚