here is the answer key
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 1
13.1 Pythagorean Theorem and its Converse
Answers
1. 194
2. 63
3. 5 3
4. c =10
5. 4 10
6. 6 5
7. Yes
8. No
9. No
10. Yes
11. No
12. No
13. ( )( ) ( ) 1 1 2 2 2
2 2
b a a b a ab b + + → + +
14. ( ) 1 11 2 2 2 2
2 22
⎛ ⎞ ⎜ ⎟ + → + ⎝ ⎠ ab c ab c
15. Students must provide proof.
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 2
13.2 Sine, Cosine and Tangent
Answers
1. 0.5736
2. 3.0777
3. 0.6691
4. 1
5. 0.5
6. 0.0349
7. 343 sin ,cos ,tan 554
NNN === ;
434 sin ,cos ,tan 553
MMM ===
8. x y ≈ ≈ 5.14, 6.13
9. x y ≈ ≈ 11.03, 4.66
10. x y ≈ ≈ 8.66, 10
11. b c ≈ ≈ 17.60, 12.87
12. c a ≈ ≈ 23.18, 6.21
13. a b ≈ ≈ 15.01, 16.56
14. 17.3ft
15. 12.7 km
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 3
13.3 Inverse Trig Functions and Solving Right Triangles
Answers
1. 44°
2. 60°
3. 81°
4. 13°
5. 61°
6. 20°
7. x y ≈ 45 , 45 ° ≈ °
8. x y ≈ 71 , 19 ° ≈ °
9. x y ≈ 27 , 63 ° ≈ °
10. x y ≈ 45 , 45 ° ≈ °
11. x y ≈ 50 , 40 ° ≈ °
12. x y ≈ 33 , 57 ° ≈ °
13. mB mA b ∠ ≈ 41 , 39 , 39.7 ° ∠ ≈ ° ≈
14. mB mA c ∠ ≈ 56 , 24 , 10.8 ° ∠ ≈ ° ≈
15. mB mA a ∠ ≈ 40 , 50 , 10.7 ° ∠ ≈ ° ≈
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 4
13.4 Application Problems
Answers
1. 11.3 in
2. 477 m
3. 35 m
4. 97 ft
5. 39°
6. 88 ft
7. 31°
8. 97 ft
9. 29 ft
10. 13 miles
11. The hypotenuse is always the longest side. Therefore, the ratios, <1 O
H
and <1 A
H .
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 5
13.5 Introduction to Angles of Rotations, Coterminal
Angles and Reference Angles
Answers
1. −458° , 262°
2. 115° , −245°
3. −570° , 150°
4. −313° , 407°
5. −302° , 58°
6. −6 , 714 ° °
7. 353 , 367 ° − °
8. QII, 78°
9. QIV, 40°
10. QIII, 47°
11. QIII, 80°
12. QIV, 56°
13. QIII, 71°
14. QIV, 12°
15. All the angles between 0° and 90° are acute angles between the terminal side of
the angle and the x-axis.
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 6
13.6 Introduction to the Unit Circle and Radian Measure
Answers
1. 3
4
π
2. 4
3
π
3. 11
6
π −
4. 5
2
π
5. 7
4
π −
6. 420°
7. −390°
8. 810°
9. −135°
10. 150°
11. coterminal angles: 2 4 , 3 3
π π − ; reference angle: 3
π QII
12. coterminal angles: 3 5 , 4 4
π π − ; reference angle: 4
π QII
13. coterminal angles: 11 13 , 6 6
π π − ; reference angle: 6
π QIV
14. coterminal angles: 10 2 , 3 3
π π − ; reference angle: 3
π QIII
15. coterminal angles: 5 7, 6 6
π π − ; reference angle: 6
π QIII
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 7
13.7 Trigonometric Ratios on the Unit Circle
Answers
1. 2
2
2. 0
3. − 3
4. 1
2
5. 1
2 −
6. 0
7. 2
2
8. 2
2 −
9. 3
3
10. 2
2 −
11. 0
12. 1
13. 3
2 −
14. Undefined
15. 1
2
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 8
13.8 Reciprocal Trigonometric Functions
Answers
1. 1.0038
2. -0.1405
3. -1.2361
4. -0.4663
5. -1.1099
6. -1.5080
7. -1.9626
8. -1.7013
9. 2 3
3 −
10. 1
11. 1
12. 2
13. -2
14. Undefined
15. 3
3 −
16. − 2
Chapter13 – TrigonometricRatios AnswerKey
CK-12AlgebraIIwithTrigonometryConcepts 9
13.9 Inverse Trigonometric Functions
Answers
1. 102.6° , 257.4°
2. 84.7° , 275.3°
3. 92.8° , 272.8°
4. 61.5° , 118.5°
5. 188.3° , 351.7°
6. 50.3° , 230.3°
7. 3.80, 5.62
8. 1.43, 4.85
9. 2.80, 5.94
10. 1.68, 4.82
11. 0.78, 3.92
12. 0.08, 3.06
13. 0, π
14. 3
4
π , 5
4
π
15. 3
4
π , 7
4
π
16.
6
π , 11
6
π
17.
6
π ,
5
6
π
18. 0 , π
19. 2
3
π , 4
3
π
20.
4
π , 3
4
π
21.
6
π , 7
6
π
