Name: ________________________ Class: ___________________ Date: __________
ID: A
Radicals and Right Triangles Unit Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. When 5 20 is written in simplest radical form, the result is k
a. 20
c. 7
b. 10
d. 4
5 . What is the value of k?
____
2. Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards, as
shown in the diagram below.
What is the length of the diagonal, in yards, that Tanya runs?
a. 50
c. 70
b. 60
d. 80
____
3. The expression 6 50 + 6 2 written in simplest radical form is
a.
b.
____
____
6 52
12 52
c.
d.
20d + 4 125d − 3 45d .
Ê
ˆ
c. ÁÁÁ 20 + 4 125 − 3 45 ˜˜˜
Ë
¯
d. 13 5d
4. Simplify the expression
a.
845d
b.
11 5d
5. Simplify the quotient
a.
b.
3
7
3
7
17 2
36 2
3
7
.
c.
21
7
d.
3
21
1
d
Name: ________________________
____
ID: A
6. Don placed a ladder against the side of his house as shown in the diagram below.
Which equation could be used to find the distance, x, from the foot of the ladder to the base of the house?
____
a.
x = 20 − 19.5
c.
x=
20 2 − 19.5 2
b.
x = 20 2 − 19.5 2
d.
x=
20 2 + 19.5 2
7. The diagram below shows right triangle UPC.
Which ratio represents the cosine of ∠U ?
15
a.
8
15
b.
17
c.
d.
2
8
15
8
17
Name: ________________________
____
ID: A
8. The center pole of a tent is 8 feet long, and a side of the tent is 12 feet long as shown in the diagram below.
If a right angle is formed where the center pole meets the ground, what is the measure of angle A to the
nearest degree?
a. 34
c. 48
b. 42
d. 56
____
9. A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below.
If the angle of elevation from the tip of the shadow to the top of the tree is 32°, what is the height of the tree
to the nearest tenth of a foot?
a. 13.2
c. 21.2
b. 15.6
d. 40.0
____ 10. The NuFone Communications Company must run a telephone line between two poles at opposite ends of a
lake, as shown in the accompanying diagram. The length and width of the lake are 75 feet and 30 feet,
respectively.
What is the distance between the two poles, to the nearest foot?
a. 105
c. 69
b. 81
d. 45
3
Name: ________________________
ID: A
Short Answer
11. Express 5 98 in simplest radical form.
Answer: _______________________
12. In right triangle ABC, AB = 20, AC = 12, BC = 16 , and m∠C = 90. Find, to the nearest degree, the measure
of ∠A.
Answer: ___________________
13. As seen in the accompanying diagram, a person can travel from New York City to Buffalo by going north
170 miles to Albany and then west 280 miles to Buffalo.
a If an engineer wants to design a highway to connect New York City directly to Buffalo, at what angle, x,
would she need to build the highway? Find the angle to the nearest degree.
b To the nearest mile, how many miles would be saved by traveling directly from New York City to Buffalo
rather than by traveling first to Albany and then to Buffalo?
4
ID: A
Radicals and Right Triangles Unit Review
Answer Section
MULTIPLE CHOICE
1. ANS:
TOP:
2. ANS:
TOP:
3. ANS:
TOP:
4. ANS:
20d
=
B
PTS: 2
Simplifying Radicals
A
PTS: 2
Pythagoras
D
PTS: 2
Operations with Radicals
D
+ 4 125d − 3 45d
4(5d) + 4 25(5d) − 3 9(5d)
= 2 5d + 4(5)
5d − 3(3) 5d
REF: 080922ia
STA: A.N.2
REF: fall0711ia
STA: A.A.45
REF: 011024ia
STA: A.N.3
Factor the radicands using perfect-square factors.
Use the Product Property of Square Roots.
= 2 5d + 20 5d − 9 5d
= 13 5d
Combine like radicals.
Feedback
A
B
C
D
The answer should have the radical sign with at least the variable as the radicand. You
cannot square the radical expression without changing its value.
Use the Product Property of Square Roots.
Factor the radicands using perfect-square factors.
Correct!
PTS: 1
DIF: Average
REF: Page 812
OBJ: 11-7.2 Simplifying Before Adding or Subtracting
NAT: 12.5.3.c
STA: A.N.3
TOP: 11-7 Adding and Subtracting Radical Expressions
1
ID: A
5. ANS: C
3
=
7
=
Ê
3 ÁÁÁÁ
ÁÁ
7 ÁÁ
Ë
21
49
=
ˆ
7 ˜˜˜˜
˜˜
7 ˜˜
¯
Multiply by a form of 1 to get a perfect-square radicand
in the denominator.
Simplify the denominator.
21
7
Feedback
A
B
C
D
6.
7.
8.
9.
10.
First, multiply by a form of 1 to get a perfect-square radicand in the denominator. Then,
simplify the denominator.
Rationalize the denominator by finding the appropriate form of 1 to multiply by.
Correct!
A quotient with a square root in the denominator is not simplified.
PTS:
OBJ:
STA:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
ANS:
TOP:
1
DIF: Basic
REF: Page 818
11-8.4 Rationalizing the Denominator
NAT: 12.5.3.c
A.N.3
TOP: 11-8 Multiplying and Dividing Radical Expressions
C
PTS: 2
REF: 060825ia
STA: A.A.45
Pythagoras
D
PTS: 2
REF: 010919ia
STA: A.A.42
Basic Trigonometric Ratios
B
PTS: 2
REF: 060816ia
STA: A.A.43
Using Trigonometry to Find an Angle
B
PTS: 2
REF: 080914ia
STA: A.A.44
Using Trigonometry to Find a Side
B
PTS: 2
REF: 010508a
STA: A.A.45
Pythagoras
SHORT ANSWER
11. ANS:
35 2
PTS: 2
12. ANS:
53
REF: fall0731ia
STA: A.N.2
PTS: 2
REF: 011032ia
STA: A.A.43
TOP: Using Trigonometry to Find an Angle
2
TOP: Simplifying Radicals
ID: A
13. ANS:
a) 59; b) 122
PTS: 4
REF: 060231a
STA: A.A.43
TOP: Using Trigonometry to Find an Angle
3