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Geometry Step-by-Step Chapter 9
Show all steps and then explain each step you used in solving the problem.
Find x.
Steps
Explanation
2. Write a similarity statement about the three triangles shown in the diagram.
3. Find SQ.
Steps
Explanation
Find the unknown side length. Simplify answers that are radicals. Tell whether the
side lengths form a Pythagorean triple.
Find the unknown side length. Simplify answers that are radicals. Tell whether the
side lengths form a Pythagorean triple.
7. 15, 20, 25
Steps
Explanation
8. Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as right, acute, or obtuse.
2, 6, 6
9. 1,2,8
Steps
Explanation
10. Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as right, acute, or obtuse.
27, 36, 45
11. Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as right, acute, or obtuse.
2.5, 1.5, 4
12. Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as right, acute, or obtuse.
12, 16, 25
13.
Steps
Explanation
Find the value of each variable. Write answers in simplest radical form.
Find the value of each variable. Write answers in simplest radical form.
Steps
Explanation
Find the sine, the cosine, and the tangent of the acute angle A of the triangle. Express each
value as a decimal rounded to four places.
17.
Find the sine, the cosine, and the tangent of the acute angle A of the triangle. Express each
value as a decimal rounded to four places.
18.
19.
Steps
Explanation
Use trigonometric ratios to find the value of each variable. Round decimals to the
nearest tenth.
21. In a college soccer league, the smallest field allowed is a rectangle 65 yards wide and
110 yards long. The largest field allowed is a rectangle 80 yards wide and 120 yards long.
To the nearest yard, how much longer is the diagonal of the largest field than the diagonal
of the smallest field?
22. Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths
form a Pythagorean triple.
23.
Steps
Explanation
24. Find the value of each variable. Write answers in simplest radical form.
ANSWERS to Geometry Step-by-Step Chapter 9:
1. 12
2.
3. 2 sqrt3
4. 2; no
5. 14; no
6. 16.5; no
7. yes; right
8. yes; acute
9. no
10. yes; right
11. no
12. yes; obtuse
13.
14.
15.
16. sin A = 0.6; cos A = 0.8; tan A = 0.75
17. sin A = 0.6; cos A = 0.8; tan A = 0.75
18. sin A = 0.4854; cos A = 0.8738; tan A = 0.5556
19. 7.2
20. 8.8
21. 16 yd.
22. 7.6; no
23.
24.