Chapter 8
Find the geometric mean between each pair of
numbers.
1. 7 and 12
ANSWER: Find x, y, and z.
3. SOLUTION: SOLUTION: ANSWER: 2. 8 and 36
SOLUTION: ANSWER: Find x, y, and z.
3. ANSWER: SOLUTION: 4. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
Page 1
Find x.
5. ANSWER: Chapter 8
4. SOLUTION: ANSWER: 6. SOLUTION: ANSWER: Find x.
5. ANSWER: SOLUTION: Determine whether each set of numbers can be
the measures of the sides of a triangle. If so,
classify the triangle as acute, obtuse, or right.
Justify your answer.
7. 24, 32, 41
ANSWER: 6. SOLUTION: First, ensure that no side is larger than the sum of the
other two sides.
41 < 24 + 32
32 < 24 + 41
24 < 32 + 41
Use the Pythagorean Theorem. If the two sides are
2
2
2
equal, it is right. If c > a + b , it is obtuse.
Otherwise, it is acute.
SOLUTION: +
1681
576 + 1024
1681 > 1600
Obtuse
ANSWER: yes; obtuse
+
ANSWER: eSolutions Manual - Powered by Cognero
Determine whether each set of numbers can be
the measures of the sides of a triangle. If so,
1681
576 + 1024
1681 > 1600
8. 17.5, 60, 62.5
Page 2
+
1681
576 + 1024
1681 > 1600
ANSWER: Chapter 8
Determine whether each set of numbers can be
the measures of the sides of a triangle. If so,
classify the triangle as acute, obtuse, or right.
Justify your answer.
7. 24, 32, 41
SOLUTION: First, ensure that no side is larger than the sum of the
other two sides.
41 < 24 + 32
32 < 24 + 41
24 < 32 + 41
Use the Pythagorean Theorem. If the two sides are
2
2
8. 17.5, 60, 62.5
SOLUTION: First, ensure that no side is larger than the sum of the
other two sides.
62.5 < 60 + 17.5
60 < 62.5 + 17.5
17.5 < 60 + 62.5
Use the Pythagorean Theorem. If the two sides are
2
2
2
equal, it is right. If c > a + b , it is obtuse.
Otherwise, it is acute.
2
equal, it is right. If c > a + b , it is obtuse.
Otherwise, it is acute.
+
3906.25
306.25 + 3600
3906.25 = 3906.25
right
+
1681
576 + 1024
1681 > 1600
Obtuse
ANSWER: yes; obtuse
ANSWER: yes; right
+
3906.25
306.25 + 3600
3906.25 = 3906.25
Find x.
9. +
1681
576 + 1024
1681 > 1600
8. 17.5, 60, 62.5
SOLUTION: First, ensure that no side is larger than the sum of the
other two sides.
62.5 < 60 + 17.5
60 < 62.5 + 17.5
17.5 < 60 + 62.5
Use the Pythagorean Theorem. If the two sides are
2
2
2
equal, it is right. If c > a + b , it is obtuse.
Otherwise, it is acute.
ANSWER: 22
+
3906.25
306.25 + 3600
3906.25 = 3906.25
eSolutions
rightManual - Powered by Cognero
ANSWER: SOLUTION: Use the rule for the 45-45-90 triangle. The two legs
are x and the hypotenuse is
.
One leg is
and we need to find the hypotenuse.
The hypotenuse is
.
10. Page 3
SOLUTION: ANSWER: Chapter
22 8
ANSWER: 10. 12. SOLUTION: Use the rule for the 30-60-90 triangle. The smallest
leg (opposite the 30) is x and the hypotenuse is 2x.
The longer leg is
.
The longer leg is 21 and we need to find the smallest
leg.
SOLUTION: Use the rule for the 45-45-90 triangle. The two legs
are x and the hypotenuse is
.
The hypotenuse is 28 and we need to find one leg.
ANSWER: Find x. Round to the nearest tenth, if
necessary.
13. ANSWER: 11. SOLUTION: SOLUTION: Use the rule for the 30-60-90 triangle. The smallest
leg (opposite the 30) is x and the hypotenuse is 2x.
The longer leg is
.
The hypotenuse is 18, so the smaller leg is 9.
Therefore, the longer leg is
ANSWER: 22.6
.
14. ANSWER: SOLUTION: 12. eSolutions Manual - Powered by Cognero
SOLUTION: Use the rule for the 45-45-90 triangle. The two legs
Page 4
ANSWER: The board should be 4 feet.
ANSWER: Chapter
22.6 8
14. ANSWER: 4 ft
16. BUILDINGS Kara is standing about 50 feet from
the base of her apartment building, looking up at it
with an angle of elevation of 75°. What is the approximate height of Kara’s building?
SOLUTION: SOLUTION: ANSWER: 13.3
ANSWER: about 187 ft
15. SKATEBOARDING Lindsey is building a skateboa
to be 1 foot tall at the end and she wants it to make a
What length of board should she buy for the ramp its
foot.
SOLUTION: The board should be 4 feet.
ANSWER: 4 ft
16. BUILDINGS Kara is standing about 50 feet from
the base of her apartment building, looking up at it
with an angle of elevation of 75°. What is the approximate height of Kara’s building?
SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: Page 5