Extra Practice for Sem 2, Quiz 6
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
5√3
60
5
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
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
x
30
9
60
18
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
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
9√3 x
30
9
60
18
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
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
I have the hyp, so get short
leg first by dividing by 2
7√2
60
14√2
30
7√6
x
Then, from the short leg to
get the long leg, multiply by
√3
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
I have the hyp, so get short
leg first by dividing by 2
6√3
60
12√3
18
x
30
Then, from the short leg to
get the long leg, multiply by
√3
6√3•√3 = 6•3 = 18
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
48
60
96 x
48√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
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
8√2
60
8√6
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 √2 = 8√2
√3
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
6√3
60
x
18
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
18 • √3 = 18√3
√3 • √3
3
= 6√3
Use special right ∆ rules to find the exact
value of x. Answers in simplified radical form
x
4√3
45
45
I have the hyp, so to
get the legs, divide by
√2
4√6√3 = 4√3
√2
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
27
x = 35.1
Use Soh Cah Toa to find the value of x.
Round to the nearest tenth.
sin (20) = 80
1
x
80
20
x=
80
sin (20)
x = 233.9
Use Soh Cah Toa to find the value of x.
Round to the nearest tenth.
tan (29) = x
1
17
29
17
x = 17tan (29)
x
x = 9.4
Use Soh Cah Toa to find the value of x.
Round to the nearest tenth.
cos(x) = 97/133
x
97
133
x = cos-1 (97/133)
x = 43.2
Use Soh Cah Toa to find the value of x.
Round to the nearest tenth.
65
41
sin (65) = x
1
41
x = 41sin (65)
x
x = 37.2
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
x = 67.4
10
24
Use Soh Cah Toa to find the value of x.
Round to the nearest tenth.
72
18
cos(72) = 18
1
x
x=
18
cos(72)
x = 58.2
Use Pythagorean Thm to find the
value of x. Round to the nearest tenth.
182 + 242 = x2
324 + 576 = x2
900 = x2
30 = x
18
24
Use Pythagorean Thm to find the
value of x. Round to the nearest tenth.
x
50
48
x2 + 482 = 502
x2 + 2304 = 2500
x2 = 196
x = 14
Use Pythagorean Thm to find the
value of x. Round to the nearest tenth.
x
20
12
x2 + 122 = 202
x2 + 144 = 400
x2 = 256
x = 16
Use Altitude-on-hypotenuse theorems to
find the value of x. Round to the nearest tenth.
x
5
x
5
5
10
10x = 25
x = 2.5
10
=
Use Altitude-on-hypotenuse theorems to
find the value of x. Round to the nearest tenth.
x
3
3
5
5x = 9
x = 1.8
x
3
=
5
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
2
x + 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.
2
9
9
12
x
+
2
12
2
x
=
2
x = 81 + 144
x2 = 225
x = 15
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?
tan (75) = x
1
40
x = 40tan (75)
x
x = 149.3’
75˚
40
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?
64
48˚
x
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?
sin(x) = 15/20
15
20
x˚
x = sin-1 (15/20)
x = 48.6