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Precalculus : Use the laws of cosines and sines

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Example Questions

Example Question #21 : Law Of Cosines And Sines

Find the length of the missing side, .

Possible Answers:

20.57

28.54

25.53

29.12

Correct answer:

25.53

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{12}{\sin 21}=\frac{16}{\sin B}$

$12\sin B = 5.73$

$\sin B=0.48$

B= 28.69

Recall that all the angles in a triangle need to add up to 180 degrees.

21+28.69+A=180

A=130.31

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 130.31}=\frac{12}{\sin 21}$

$d \sin 21= 9.15$

d=25.53

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Example Question #22 : Law Of Cosines And Sines

Find the length of the missing side, .

Possible Answers:

10.73

8.14

9.89

12.44

Correct answer:

10.73

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{6}{\sin34}=\frac{9}{\sin B}$

$6 \sin B = 5.03$

$\sin B=0.84$

B= 57.14

Recall that all the angles in a triangle need to add up to 180 degrees.

34+57.14+A=180

A=88.86

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 88.86}=\frac{6}{\sin 34}$

$d \sin 34=5.9988$

d=10.73

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Example Question #23 : Law Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

13.98

14.63

15.12

12.37

Correct answer:

14.63

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{13}{\sin 54}=\frac{14}{\sin B}$

$13\sin B = 11.33$

$\sin B=0.87$

B= 60.46

Recall that all the angles in a triangle need to add up to 180 degrees.

54+60.46+C=180

C=65.54

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 65.54}=\frac{13}{\sin 54}$

$d \sin 54= 11.83$

d=14.63

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Example Question #24 : Law Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

8.95

8.81

9.51

7.84

Correct answer:

8.95

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{6}{\sin 41}=\frac{8}{\sin B}$

$6\sin B = 5.25$

$\sin B=0.875$

B= 61.04

Recall that all the angles in a triangle need to add up to 180 degrees.

41+61.04+C=180

C=77.96

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 77.96}=\frac{6}{\sin 41}$

$d \sin 41= 5.87$

d=8.95

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Example Question #25 : Law Of Cosines And Sines

Find the length of the missing side, .

Possible Answers:

19.35

11.71

15.62

14.12

Correct answer:

15.62

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{9}{\sin 35}=\frac{12}{\sin B}$

$9\sin B = 6.88$

$\sin B=0.76$

B= 49.46

Recall that all the angles in a triangle need to add up to 180 degrees.

35+49.46+C=180

C=95.54

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 95.54}=\frac{9}{\sin 35}$

$d \sin 35= 8.96$

d=15.62

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Example Question #26 : Law Of Cosines And Sines

Find the length of the missing side, .

Possible Answers:

20.18

27.98

28.91

24.71

Correct answer:

27.98

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{17}{\sin 33}=\frac{16}{\sin C}$

$17\sin C = 8.71$

$\sin C= 0.51$

C= 30.66

Recall that all the angles in a triangle need to add up to 180 degrees.

33+30.66+B=180

B=116.34

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 116.34}=\frac{17}{\sin 33}$

$d \sin 33= 15.24$

d=27.98

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Example Question #27 : Law Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

24.12

35.91

29.07

31.50

Correct answer:

31.50

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{19}{\sin 37}=\frac{24}{\sin C}$

$19\sin C = 14.44$

$\sin C= 0.76$

C= 49.46

Recall that all the angles in a triangle need to add up to 180 degrees.

37+49.46+B=180

B=93.54

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 93.54}=\frac{19}{\sin 37}$

$d \sin 37 = 18.96$

d=31.50

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Example Question #28 : Law Of Cosines And Sines

Find the length of the missing side, .

Possible Answers:

10.25

9.92

7.64

9.28

Correct answer:

10.25

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{7}{\sin 29}=\frac{4}{\sin C}$

$7\sin C = 1.94$

$\sin C= 0.28$

C= 16.26

Recall that all the angles in a triangle need to add up to 180 degrees.

16.26+29+B=180

B=134.74

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 134.74}=\frac{7}{\sin 29}$

$d \sin 29= 4.97$

d=10.25

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Example Question #29 : Law Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

16.29

18.19

17.14

17.80

Correct answer:

17.14

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{19}{\sin 61}=\frac{20}{\sin B}$

$19\sin B = 17.49$

$\sin B=0.92$

B= 66.93

Recall that all the angles in a triangle need to add up to 180 degrees.

61+66.93+C=180

C=52.07

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 52.07}=\frac{19}{\sin 61}$

$d \sin 61= 14.99$

d=17.14

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Example Question #71 : Trigonometric Applications

Find the length of the missing side, .

Possible Answers:

11.13

13.22

14.13

15.92

Correct answer:

14.13

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{13}{\sin 64}=\frac{9}{\sin C}$

$13\sin C = 8.09$

$\sin C=0.62$

C= 38.32

Recall that all the angles in a triangle need to add up to 180 degrees.

64+38.32+B=180

B=77.68

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 77.68}=\frac{13}{\sin 64}$

$d \sin 64= 12.70$

d=14.13

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Precalculus : Use the laws of cosines and sines

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #21 : Law Of Cosines And Sines

Example Question #22 : Law Of Cosines And Sines

Example Question #23 : Law Of Cosines And Sines

Example Question #24 : Law Of Cosines And Sines

Example Question #25 : Law Of Cosines And Sines

Example Question #26 : Law Of Cosines And Sines

Example Question #27 : Law Of Cosines And Sines

Example Question #28 : Law Of Cosines And Sines

Example Question #29 : Law Of Cosines And Sines

Example Question #71 : Trigonometric Applications

All Precalculus Resources

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