Bo is building a tree house. He has marked locations for four holes that will hold his corner
posts. They form a figure with a long side of 12
'feet and a short side of 9 feet. What must the
diagonal of the figure be to make sure the base
of his tree house is a rectangle?

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

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.