Transcript Chapter 8 Review

Chapter 8 Review
Practice problems for the chapter 8 exam.
1
1. Find the length of the missing side. The
triangle is not drawn to scale.
A. 48
B. 10
6
C. 28
8-1
D. 100
69%
8
19%
2
13%
0%
A.
B.
C.
D.
1. Find the length of the missing side. The
triangle is not drawn to scale.
2
6
8-1
8
2
2
𝑎 +𝑏 =𝑐
62 + 82 = 𝑐 2
36 + 64 = 𝑐 2
100 = 𝑐 2
100 = c
10 = 𝑐
Correct answer is B.
3
2. Triangle ABC has side lengths 3, 4, and 5. Do the
side lengths form a Pythagorean triple? Explain.
A.
B.
C.
D.
8-1
No, they do not form a Pythagorean triple; although , the side lengths
do not meet the other requirements of a Pythagorean triple.
Yes; they can form a right triangle, so they form a Pythagorean triple.
Yes, they form a Pythagorean triple; 32 + 42 = 52 and 3, 4, and 5 are
all nonzero whole numbers.
No, they do not form a Pythagorean triple; 32 + 42 ≠ 52 .
44%
19%
19%
19%
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A.
B.
C.
D.
2. Triangle ABC has side lengths 3, 4, and 5. Do the
side lengths form a Pythagorean triple? Explain.
8-1
Since 3, 4, and 5 are all nonzero whole
numbers
AND 32 + 42 = 52
Correct answer is C. Yes, they form a
Pythagorean triple; 32 + 42 = 52 and 3, 4,
and 5 are all nonzero whole numbers.
5
3. Find the length of the missing side. Leave your
answer in simplest radical form.
13 ft
8-1
10 ft
A.
69 ft
B.
269 ft
C.
23 ft
D.
3 ft
50%
Not drawn to scale
25%
13%
A.
B.
13%
C.
D.
6
3. Find the length of the missing side. Leave your
answer in simplest radical form.
𝑎2 + 𝑏2 = 𝑐 2
102 + 𝑏 2 = 132
13 ft
100 + 𝑏 2 = 169
8-1
10 ft
𝑏 2 = 69
Not drawn to scale
𝑏 = 69
7
Correct answer is A.
69 ft
4. A triangle has sides of lengths 27, 79, and 84.
Is it a right triangle? Explain.
8-1
A.
B.
C.
D.
yes; 272 + 792 = 842
no; 272 + 792 = 842
yes; 272 + 792 ≠ 842
no; 272 + 792 ≠ 842
75%
8
13%
13%
B.
C.
0%
A.
D.
4. A triangle has sides of lengths 27, 79, and 84.
Is it a right triangle? Explain.
𝑎2 + 𝑏 2 ⎕𝑐 2
If it is equal then the triangle is a right triangle.
8-1
272 + 792 ⎕842
729 + 6241⎕7056
6970⎕7056
6970 ≠ 7056
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Correct answer is D. no; 272 + 792 ≠ 842
5. A triangle has side lengths of 23 in, 6 in, and 28 in.
Classify it as acute, obtuse, or right.
A. obtuse
B. right
C. acute
8-1
50%
44%
10
6%
A.
B.
C.
5. A triangle has side lengths of 23 in, 6 in, and 28 in.
Classify it as acute, obtuse, or right.
𝑐 2 ⎕ 𝑎2 + 𝑏2
If it is less then the triangle is an acute triangle.
If it is more then the triangle is an obtuse triangle.
If it is equal then the triangle is a right triangle.
8-1
282 ⎕ 232 + 62
784 ⎕ 529 + 36
784⎕565
784 > 565
Correct answer A. Obtuse
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6. In triangle ABC, ∠𝐴 is a right angle and ∠𝐵 = 45°.
Find BC. If your answer is not an integer, leave it in
simplest radical form. C
A. 10 2 ft
8-2
B. 20 2 ft
10 ft C. 10 ft
D. 20 ft
B
A
Not drawn to scale
38%
31%
25%
6%
A.
B.
C.
D.
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6. In triangle ABC, ∠𝐴 is a right angle and ∠𝐵 = 45°.
Find BC. If your answer is not an integer, leave it in
simplest radical form.
In a 45-45-90 both legs are the
C
same value
8-2
10 ft the hypotenuse is leg * 2
Since the leg is 10
B
A
Not drawn to scale
The hypotenuse is 10 2
The correct answer is A. 10 2
13
7. Find the value of the variable. If your
answer is not an integer, leave it in simplest
radical form.
5 3
A.
45°
2
x
5
8-2
Not drawn to scale
31%
19%
B. 5 3
C. 5 2
D.
5 2
2
31%
19%
14
A.
B.
C.
D.
7. Find the value of the variable. If your
answer is not an integer, leave it in simplest
radical form.
45°
x
8-2
5
The get back to the leg of a
45-45-90 given the
hypotenuse you must
divide by 2
5
2
Not drawn to scale
Will simplify to
5 2
2
Correct answer is D.
5 2
2
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8. Find the value of the variable(s). If your answer is
not an integer, leave it in simplest radical form.
A. 5 3
5
x
60°
8-2
10
Not drawn to scale
B.
1
2
C. 10 3
D. 2
44%
44%
6%
A.
B.
6%
C.
D.
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8. Find the value of the variable(s). If your answer is
not an integer, leave it in simplest radical form.
5
x
60°
8-2
10
Not drawn to scale
In a 30-60-90 right triangle everything is based off the short leg.
Hypotenuse is twice the short leg and long leg is short leg * 3
The short leg is 5 so the long leg is 5 3
Correct answer is A. 5 3
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9. Find the value of the variable(s). If your answer
is not an integer, leave it in simplest radical form.
8-2
A. x = 22 3, y = 11
y
11
30°
x
Not drawn to scale
B. x = 11 3, y = 22
C. x = 22, y = 11 3
D. x = 11, y = 22 3
63%
31%
18
6%
0%
A.
B.
C.
D.
9. Find the value of the variable(s). If your answer
is not an integer, leave it in simplest radical form.
8-2
y
11
30°
x
Not drawn to scale
In a 30-60-90 right triangle everything is based off the short leg.
Hypotenuse is twice the short leg and long leg is short leg * 3
The short leg is 11 so the long leg is 11 3 and the hypotenuse is 22.
Correct answer is B. x = 11 3, y = 22
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10. The length of the hypotenuse of a 30°–60°–90°
triangle is 9. Find the perimeter.
A. 27 + 9 3
B.
8-2
C.
27
9
+
2
2
9
27
+
2
2
3
3
D. 9 + 27 3
38%
31%
19%
13%
20
A.
B.
C.
D.
8-2
10. The length of the hypotenuse of a 30°–60°–90°
triangle is 9. Find the perimeter.
In a 30-60-90 right triangle everything is based off the short leg.
Since they give you the hypotenuse and the hypotenuse is twice
9
the short leg the short leg is .
2
The long leg is short leg * 3 so it is
9
2
3.
The perimeter is the sum of all three sides
9 9
27
9
9+ + 3 =
+
3.
2
2
2
Correct answer is B.
2
27
2
+
9
2
21
3
11. Find the missing value to the nearest hundredth.
cos
8-3
2
= 5
A.
B.
C.
D.
23.58o
66.42o
21.8o
63.21o
38%
38%
19%
6%
A.
B.
C.
D.
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11. Find the missing value to the nearest hundredth.
cos
2
= 5
8-3
To find degrees we use the inverse functions.
𝑐𝑜𝑠 −1
2
5
23
The correct answer is B. 66.42o
12. Use a trigonometric ratio to find the value of
x. Round your answer to the nearest tenth.
x
A.
B.
C.
D.

8-3
2.6
4.8
3.4
3.1
4
56%
Not drawn to scale
19%
13%
A.
24
13%
B.
C.
D.
12. Use a trigonometric ratio to find the value of
x. Round your answer to the nearest tenth.
x
Figure out which trigonometric ratio you need.

Tangent we have opposite leg and adjacent leg
8-3
4
𝑡𝑎𝑛40 =
𝑥
𝑜
4
Variable is in the bottom so we divide by the trig function.
Not drawn to scale
4
𝑥=
= 4.8
𝑡𝑎𝑛40𝑜
The correct answer is B. 4.8
25
13. Find the value of x. Round to the nearest tenth.
x

8-3
A.
B.
C.
D.
14.5
10.7
10.2
14.2
12
31%
Not drawn to scale
25%
25%
19%
26
A.
B.
C.
D.
8-3
13. Find the value of x. Round to the nearest tenth.
x

12
Figure out which trigonometric ratio you need.
Not drawn to scale
Cosine we have adjacent leg and hypotenuse
12
𝑐𝑜𝑠32 =
𝑥
𝑜
Variable is in the bottom so we divide by the trig function.
12
𝑥=
= 14.15014084
𝑐𝑜𝑠32𝑜
The correct answer is D. 14.2
27
14. Find the value of x. Round to the nearest tenth.
19
x

8-3
Not drawn to scale
A.
B.
C.
D.
55.6
55.8
6.7
6.5
44%
38%
13%
6%
A.
B.
C.
D.
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14. Find the value of x. Round to the nearest tenth.
19
x

Not drawn to scale
8-3
Figure out which trigonometric ratio you need.
Sine we have opposite leg and hypotenuse
19
𝑠𝑖𝑛20 =
𝑥
𝑜
Variable is in the bottom so we divide by the trig function.
19
𝑥=
= 55.5522836
𝑠𝑖𝑛20𝑜
The correct answer is A. 55.6
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15. Find the value of x. Round to the nearest degree.
20
x
8-3
11
A.
B.
C.
D.
60
57
29
33
Not drawn to scale
38%
31%
19%
13%
30
A.
B.
C.
D.
15. Find the value of x. Round to the nearest degree.
20
x
11
Figure out which trigonometric ratio you need.
Not drawn to scale
8-3
Cosine we have adjacent leg and hypotenuse
𝑐𝑜𝑠𝑥 𝑜 =
11
20
We are looking for degrees so we use the inverse function.
𝑐𝑜𝑠 −1
11
= 56.63298703
20
The correct answer is B. 57 degrees.
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16. What is the description of ∠2 as it relates to the situation shown?
38%
1
5
25%
25%
2
3
4
8-4
A.
B.
C.
D.
13%
A.
B.
C.
D.
∠2 is the angle of depression from the airplane to the radar tower.
∠2 is the angle of elevation from the airplane to the radar tower.
∠2 is the angle of elevation from the radar tower to the airplane.
∠2 is the angle of depression from the radar tower to the airplane.
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16. What is the description of ∠2 as it relates to the situation shown?
1
5
2
3
4
8-4
Since Angle 2 goes up from the radar tower, it is
an angle of elevation
and it goes from the radar tower to the airplane
The correct answer is C. ∠2 is the angle of
elevation from the radar tower to the airplane.
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17. Find the value of x. Round the length to the nearest tenth.
A.
B.
C.
D.
8 ft

8-4
x
6.5 ft
4.7 ft
9.9 ft
5.8 ft
Not drawn to scale
50%
38%
34
6%
A.
B.
6%
C.
D.
17. Find the value of x. Round the length to the nearest tenth.
8 ft

x
Figure out which trigonometric ratio you need.
Not drawn to scale
8-4
Cosine we have adjacent leg and hypotenuse
𝑐𝑜𝑠
36𝑜
𝑥
=
8
Variable is in the top so we multiply by the trig function.
𝑥 = 8 ∗ 𝑐𝑜𝑠36𝑜 = 6.472135955
35
The correct answer is A. 6.5 ft
18. Find the value of x. Round the length to the nearest tenth.

A.
B.
C.
D.
x
500 m
777.9 m
595.9 m
321.4 m
652.7 m
8-4
Not drawn to scale
63%
19%
13%
6%
A.
B.
C.
D.
36
18. Find the value of x. Round the length to the nearest tenth.

x
500 m
Not drawn to scale
Move the angle and figure out which trigonometric ratio you need.
8-4
Sine we have opposite leg and the hypotenuse
𝑠𝑖𝑛
40𝑜
500
=
𝑥
Variable is in the bottom so we divide by the trig function.
𝑥=
500
= 777.8619134
𝑜
sin 40
The correct answer is A. 777.9 m
37
19. Find the value of x. Round the length to the nearest tenth.
A.
B.
C.
D.

x
8-4
4.6 yd
10 yd
23.6 yd
5.1 yd
11 yd
Not drawn to scale
38
0%
A.
0%
B.
0%
C.
0%
D.
19. Find the value of x. Round the length to the nearest tenth.

x
11 yd
8-4
Not drawn to scale
Move the angle and figure out which
trigonometric ratio you need.
Tangent we have opposite leg and adjacent leg
𝑡𝑎𝑛
25𝑜
𝑥
=
11
Variable is in the top so we multiply by the trig
function.
𝑥 = 11 ∗ 𝑡𝑎𝑛25𝑜 = 5.12938424
The correct answer is D. 5.1 yd
39
20. To approach the runway, a pilot of a small plane must begin a 10o descent starting
from a height of 1983 feet above the ground. To the nearest tenth of a mile, how many
miles from the runway is the airplane at the start of this approach?

1983 ft
x
8-4
A.
B.
C.
D.
2.2 mi
0.4 mi
11,419.6 mi
2.1 mi
Not drawn to scale
40
0%
A.
0%
B.
0%
C.
0%
D.
20. To approach the runway, a pilot of a small plane must begin a 10o descent starting
from a height of 1983 feet above the ground. To the nearest tenth of a mile, how many
miles from the runway is the airplane at the start of this approach?
Move the angle and figure out which
trigonometric ratio you need.

1983 ft
8-4
x
Sine we have opposite leg and the hypotenuse
Not drawn to scale
𝑠𝑖𝑛 10𝑜 =
1983
𝑥
Variable is in the bottom so we divide by the
trig function.
1983
𝑥=
= 11419.64187 𝑓𝑒𝑒𝑡
𝑠𝑖𝑛 10𝑜
To convert to miles divide by 5280 = 2.1628
The correct answer is A. 2.2 mi
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