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Extra Practice for Sem 2, Quiz 6
5√360
5
30
I have the short leg, so to getlong leg, multiply by √3
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
x
45
16
16√2
45
I have a leg, so to get the hyp, multiply by √2
x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
30
189
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
x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
9√330
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
x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
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 √3x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
18
60
12√3
6√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
6√3•√3 = 6•3 = 18
x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
96
60
48√3
48
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
x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
16√2
60
8√6
8√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
8√6 √3
√2 = 8√2
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
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 • √3
= 18√3 3
18 √3
= 6√3
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
x
4√3
45
4√6
45
I have the hyp, so to get the legs, divide by √2
4√6 √2
√3 = 4√3x
Use special right ∆ rules to find the exact value of x. Answers in simplified radical form
33 cos(x) = 27/33
x = cos-1 (27/33)
x = 35.127
x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
8020
sin (20) = 80
1 x
x = 80 sin (20)
x = 233.9
x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
1729
tan (29) = x
1 17
x = 17tan (29)
x = 9.4x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
133
cos(x) = 97/133
x = cos-1 (97/133)x = 43.2
97
x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
4165
sin (65) = x
1 41
x = 41sin (65)
x = 37.2x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
24
tan(x) = 24/10
x = tan-1 (24/10)
x = 67.410
x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
1872
cos(72) = 18
1 x
x = 18 cos(72)
x = 58.2
x
Use Soh Cah Toa to find the value of x. Round to the nearest tenth.
18
182 + 242 = x2
324 + 576 = x2
900 = x2
30 = x
x
Use Pythagorean Thm to find the value of x. Round to the nearest tenth.
24
50x2 + 482 = 502
x2 + 2304 = 2500 x2 = 196 x = 14x
Use Pythagorean Thm to find the value of x. Round to the nearest tenth.
48
20x2 + 122 = 202
x2 + 144 = 400 x2 = 256 x = 16x
Use Pythagorean Thm to find the value of x. Round to the nearest tenth.
12
5x 10
x = 5 5 10 10x = 25 x = 2.5
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
3
x5
x = 3 3 5 5x = 9 x = 1.8
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x
8 12
x = 8 8 x + 12 x2 + 12x = 64 x2 + 12x – 64 = 0 (x – 4)(x + 16) = 0 x = 4 x = -16
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
x
6 5
x = 6 6 x + 5 x2 + 5x = 36 x2 + 5x – 36 = 0 (x – 4)(x + 9) = 0 x = 4 x = -9
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
9
x
12
92 + 122 = x2
x2 = 81 + 144 x2 = 225 x = 15
Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth.
Factor.
x2 + 12x + 32
(x + 4)(x + 8)
Factor
x2 – 12x + 32
(x – 4)(x – 8)
Factor
x2 – 4x + 32
(x + 4)(x – 8)
Factor
x2 + 14x + 45
(x + 9)(x + 5)
Factor
x2 + 15x + 36
(x + 12)(x + 3)
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?
x
4075˚
tan (75) = x
1 40
x = 40tan (75)
x = 149.3’
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?
x
64
48˚
cos (48) = x
1 64
x = 64cos(48)
x = 42.8yds
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?
2015
x˚
sin(x) = 15/20
x = sin-1 (15/20)
x = 48.6
