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MATH 8
CHAPTER 9 REVIEW
REAL NUMBERS AND RIGHT TRIANGLES
1
Find the value of the variable. Round to the nearest hundredth.
63°
12.3 cm
y
2
The lengths of two sides of a right triangle are given. Find the length of the third side.
a = 8, c = 17
3
Simplify the expression.
√48xy2
4
Find the trigonometric ratio as a fraction in simplest form.
cos B
B
7
A
24
C
5
Is √143 a rational or an irrational number?
6
Simplify the expression.
72
√ 25
7
Solve the equation. Round to the nearest tenth when necessary.
146 = h2
8
Approximate the tangent value to four decimal places.
tan 63°
9
Approximate the value to four decimal places.
sin 35°
10
Approximate the tangent value to four decimal places.
tan 85°
11
Find the distance between the points A and B.
12
Evaluate the expression when x = 16 and y = 25.
– √xy
13
Find the unknown lengths. Write your answers in simplest form.
45°
5√2
y
45°
x
14
Approximate the value to four decimal places.
sin 99°
15
Find the unknown side lengths in each triangle if ∆JKL ~ ∆MNP. Write your answers in
simplest form.
K
N
60°
14 in.
8 in.
30°
M
J
16
L
Find the unknown lengths. Write your answer in simplest form.
K
y
9 in.
J
45°
x
M
P
17
Order the numbers from least to greatest.
0.89, 17 , √0.81, 2√2, 1.5
19
18
Approximate the square root to the nearest integer.
√12
19
The expression √(6 – 5)2 + (2 – 8)2 represents the distance between two points. Name
the coordinates of the points.
20
Simplify the expression.
4
√ 121
21
Find the midpoint of the segment with the given endpoints.
(-3, -17), (-18, -10)
22
A ladder leans against a building, forming an angle of 57° with the ground. The top of
the ladder touches the building at a height of 6.16 meters. How far is the base of the
ladder from the building?
6.16m
57°
23
Find the unknown length. Express your answer in simplest form.
31m
c
31m
24
Which of the following sets of numbers do not represent the sides of a right triangle?
12, 16, 20
25
8, 12, 16
Complete the statement with <, >, or =.
2
7
4
? √ 49
7, 24, 25
24, 32, 40