Download Geometry Diff_Ch 8_Test Review Answers

Geometry Chapter 8 Test Review
1.
Name: ________KEY____________
Solve for x, write your answer as a whole number, fraction or a reduced radical. No Decimals!
a.
b.
x
c.
x
8
14
2 5
x+4
6
6 3
2
x 2 = 14 2 + 8 2
x2 = 6 3
x 2 = 196 + 64
x 2 = 108 + 20
x = 260
x = 128
x = 4 ⋅ 65
x = 64 ⋅ 2
x = 2 65
x =8 2
(
) + (2 5 )
x+2
2
( x + 4 ) 2 = ( x + 2) 2 + 6 2
x 2 + 8x + 16 = x 2 + 4 x + 4 + 36
4 x = 24
x =6
2.
Tell whether the following sets of values are for a right, acute or obtuse triangle. Show your
equation and work to support your answer!
€
€
a.
24, 70, 75
€
b.
28, 45, 50
75 2 ? 24 2 + 70 2
5625 ? 576 + 4900
50 2 ? 28 2 + 45 2
2500 ? 784 + 2025
5625 > 5476
Obtuse
2500 < 2809
Acute
4.
€
c.
5,2 3 , 37
2
37 ? 52 + 2 3
(
)
2
37? 25 +12
37 = 37
Right
Find the length of the diagonal stick in the box below; write
your answer as a whole
€ number, or as a reduced radical.
9
6"
36 2 + 12 2 + 9 2 = x 2
1296 + 144 + 81 = x 2
x = 1521
x = 39
5.
€
24"
36
You run 15 blocks east, then 8 blocks north, then 9 blocks east, then 1 block south. How far are
you from your starting point? Write your answer as a whole number, or as a reduced radical.
x 2 = 7 2 + 24 2
x 2 = 49 + 576
x = 625 = 25
€
8"
12
6.
Find the perimeter of a rectangle that has one side of 20 cm and a diagonal of 29 cm.
x 2 + 20 2 = 29 2
Perimeter = 2(20) + 2(21)
x 2 + 400 = 841
Perimeter = 82
x = 441 = 21
7.
Find a value for x and y in the following triangles, write your answer as a whole number, or as a
€
reduced radical.
a.
x = 9, y = 9 2
€
b.
y
€9
x = 11, y = 11
45º
y
y
e.
x = 6, y = 12
f.
y
y
x
7
€
x = 7 3 , y = 14 3
x
y
€
30º
30º
30º
21
6 3
x
For the following, write a trigonometric proportion, and then solve for x. Write your answer to the
nearest tenth.
a.
b.
c.
x
x
x
47o
42
32o
71
19
cos 32 =
x
tan 47 =
71
x = 71tan 47
x ≈ 76.1
€
€
45º
x = 7 3 , y = 14
8.
14
x
€
x
€
x = 7 2, y = 7 2
11 2
x
45º
d.
c.
34o
19
x
sin 34 =
19
cos 32
x ≈ 22.4
42
sin 34
x ≈ 75.1
x=
€
42
x
x=
€
d.
e.
f.
97
47
47
22
22
cos x =
47
sin x =
( )
61
97
( )
58
47
( )
x = cos−1 22
47
61
x = sin−1 97
x = tan−1 58
47
x ≈ 62.1°
x ≈ 39°
x ≈ 51°
Chris and Pat are trying to determine the height of a tree. Chris
uses an angle of elevation of 50o to see the top of the tree. Pat,
who is standing 10 feet behind Chris, uses an angle of 48o to see
the top of the tree. How tall is the tree?
tan 50 =
x
y
x
y=
tan 50
y = .8391x
10.
x
10 + y
x
10 + y =
tan 48
y = .9004 x − 10
tan 48 =
.9004 x − 10 = .8391x
.0613x = 10
x = 163.1 feet
Eartha Diggs stands atop a pyramid and spots her coworker on the ground below. Eartha uses a
42o angle of depression to see her€coworker. If she knows the
€
pyramid is 200 meter high, how far is she from her coworker?
200
x
200
x=
sin 42
x ≈ 298.9 m
sin 42 =
11.
Fireman Fred, who is 6 feet tall, stands 30 feet from a tree with a
cat caught up in the branches. Fred uses a 50o angle of elevation
from his eyes to see the cat. How far up in the tree is the cat?
x
30
x = 30 tan 50
x ≈ 35.8
tan 50 =
€
tan x =
Draw a sketch, if needed, then write a trigonometric proportion and solve. Write your final answer to
the nearest tenth.
€
€
9.
€
xo
xo
xo
€
58
61
Height = 35.8 + 6 = 41.8 feet
12.
Pat has set a ladder against the house. The ladder is 32 feet long and reaches 25 feet in the air.
What is the angle of elevation for the ladder?
sin x =
25
32
( )
25
x = sin−1 32
x ≈ 51.4°
13.
€
Chris and Taylor are standing at the bottom of a hill. Chris runs up the hill and covers a distance
of 380 feet. The hill is known to be 70 feet high. What angle of depression does Chris use to look
back down to Taylor?
sin x =
70
380
( )
70
x = sin−1 380
x ≈ 10.6°
14.
€
Pat looks to the left to see Chris who is 85 feet away. Pat then turns 70o to the right to see Sam
who is 60 feet from Pat. How far apart are Chris and Sam?
x 2 = 60 2 + 85 2 − 2(60)(85) cos 70
x 2 = 7336.395
x ≈ 85.6 feet
15.
€
A cat and a dog spy their owner in between them. The cat is 45 feet from the owner and will use a
20o angle to reach the owner. The dog will use a 30o to reach the owner, how far is the dog from
the owner?
sin 20 sin 30
=
x
45
x sin 30 = 45 sin 20
45 sin 20
x=
sin 30
x ≈ 30.8 feet
€