Chapter 13 (PDF)

7. RS 22.5 cm, EB 20 cm
8. x 20 cm; y 7.2 cm
9. p 16
3
5.3 cm; q 8
3 2.6 cm
LESSON 12.1 • Trigonometric Ratios
1. sin P p
r
2. cos P q
r
3. tan P p
q
4. sin Q q
r
5. sin T 0.800 6. cos T 0.600
7. tan T 1.333 8. sin R 0.600
9. x 12.27 10. x 29.75
11. x 18.28 12. mA 71°
13. mB 53° 14. mC 30°
w
15. sin 40° ; 28
w 18.0 cm
x
16. sin 28° ; 14
x 7.4 cm
17. cos 17° 7 y 3 ; y 76.3 cm
18. a 28° 19. t 47° 20. z 76°
LESSON 12.2 • Problem Solving with Right Triangles
1. Area 2 cm 2 2. Area 325 ft 2
3. Area 109 in 2 4. x 54.0°
5. y 31.3° 6. a 7.6 in.
7. Diameter 20.5 cm 8. 45.2°
9. 28.3° 10. About 2.0 m
11. About 445.2 ft 12. About 22.6 ft
LESSON 12.3 • The Law of Sines
1. Area 46 cm 2 2. Area 24 m 2 3. Area 45 ft 2
4. m 14 cm 5. p 17 cm 6. q 13 cm
7. mB 66°, mC 33°
8. mP 37°, mQ 95°
9. mK 81°, mM 21°
10. Second line: about 153 ft, between tethers: about 135 ft
LESSON 12.4 • The Law of Cosines
1. t 13 cm 2. b 67 cm
3. w 34 cm
4. mA 76°, mB 45°, mC 59°
5. mA 77°, mP 66°, mS 37°
6. mS 46°, mU 85°, mV 49°
7. About 24° 8. About 43.0 cm
9. About 34.7 in.
LESSON 12.5 • Problem Solving with Trigonometry
1. About 2.85 mi/h; about 15°
2. mA 50.64°, mB 59.70°, mC 69.66°
3. About 8.0 km from Tower 1, 5.1 km from Tower 2
4. About 853 miles
5. About 530 ft of fencing; about 11,656 ft 2
LESSON 13.1 • The Premises of Geometry
1. a. Given
b. Distributive property
c. Subtraction property
d. Addition property
e. Division property
2. False
3. False
4. True; transitive property of congruence and
definition of congruence
5.
A
AB CD
Given
AP CQ
Given
A
LESSON 13.2 • Planning a Geometry Proof
Proofs may vary.
1. Flowchart Proof
AB CD
Given
AP CQ
Given
M
B P
B
D
ABP CDQ
CA Postulate
PB QD
Given
APB CQD
CA Postulate
ABP CDQ
CA Postulate
APQ CQD
CA Postulate
ABP CDQ
ASA Postulate
AB CD
CPCTC
PAB QCD
Third Angle
Theorem
Discovering Geometry Practice Your Skills ANSWERS 113
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