Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #61 : Trigonometric Applications

Find the length of the missing side, \displaystyle d.

3

Possible Answers:

\displaystyle 29.12

\displaystyle 28.54

\displaystyle 25.53

\displaystyle 20.57

Correct answer:

\displaystyle 25.53

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 12\sin B = 5.73

\displaystyle \sin B=0.48

\displaystyle B= 28.69

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

\displaystyle 21+28.69+A=180

\displaystyle A=130.31

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

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

\displaystyle d \sin 21= 9.15

\displaystyle d=25.53

 

Example Question #61 : Trigonometric Applications

Find the length of the missing side, \displaystyle d.

1

Possible Answers:

\displaystyle 10.73

\displaystyle 9.89

\displaystyle 8.14

\displaystyle 12.44

Correct answer:

\displaystyle 10.73

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 6 \sin B = 5.03

\displaystyle \sin B=0.84

\displaystyle B= 57.14

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

\displaystyle 34+57.14+A=180

\displaystyle A=88.86

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

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

\displaystyle d \sin 34=5.9988

\displaystyle d=10.73

 

Example Question #21 : Use The Laws Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

7

Possible Answers:

\displaystyle 13.98

\displaystyle 12.37

\displaystyle 14.63

\displaystyle 15.12

Correct answer:

\displaystyle 14.63

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 13\sin B = 11.33

\displaystyle \sin B=0.87

\displaystyle B= 60.46

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

\displaystyle 54+60.46+C=180

\displaystyle C=65.54

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

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

\displaystyle d \sin 54= 11.83

\displaystyle d=14.63

 

Example Question #22 : Use The Laws Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

8

Possible Answers:

\displaystyle 8.95

\displaystyle 9.51

\displaystyle 8.81

\displaystyle 7.84

Correct answer:

\displaystyle 8.95

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 6\sin B = 5.25

\displaystyle \sin B=0.875

\displaystyle B= 61.04

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

\displaystyle 41+61.04+C=180

\displaystyle C=77.96

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

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

\displaystyle d \sin 41= 5.87

\displaystyle d=8.95

 

Example Question #25 : Law Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

9

Possible Answers:

\displaystyle 15.62

\displaystyle 19.35

\displaystyle 14.12

\displaystyle 11.71

Correct answer:

\displaystyle 15.62

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 9\sin B = 6.88

\displaystyle \sin B=0.76

\displaystyle B= 49.46

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

\displaystyle 35+49.46+C=180

\displaystyle C=95.54

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

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

\displaystyle d \sin 35= 8.96

\displaystyle d=15.62

 

Example Question #23 : Use The Laws Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

4

Possible Answers:

\displaystyle 20.18

\displaystyle 24.71

\displaystyle 27.98

\displaystyle 28.91

Correct answer:

\displaystyle 27.98

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle C.

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

\displaystyle 17\sin C = 8.71

\displaystyle \sin C= 0.51

\displaystyle C= 30.66

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

\displaystyle 33+30.66+B=180

\displaystyle B=116.34

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

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

\displaystyle d \sin 33= 15.24

\displaystyle d=27.98

 

Example Question #27 : Law Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

5

Possible Answers:

\displaystyle 35.91

\displaystyle 24.12

\displaystyle 31.50

\displaystyle 29.07

Correct answer:

\displaystyle 31.50

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle C.

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

\displaystyle 19\sin C = 14.44

\displaystyle \sin C= 0.76

\displaystyle C= 49.46

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

\displaystyle 37+49.46+B=180

\displaystyle B=93.54

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

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

\displaystyle d \sin 37 = 18.96

\displaystyle d=31.50

 

Example Question #21 : Use The Laws Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

6

Possible Answers:

\displaystyle 9.92

\displaystyle 9.28

\displaystyle 10.25

\displaystyle 7.64

Correct answer:

\displaystyle 10.25

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle C.

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

\displaystyle 7\sin C = 1.94

\displaystyle \sin C= 0.28

\displaystyle C= 16.26

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

\displaystyle 16.26+29+B=180

\displaystyle B=134.74

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

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

\displaystyle d \sin 29= 4.97

\displaystyle d=10.25

 

Example Question #29 : Law Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

10

Possible Answers:

\displaystyle 17.14

\displaystyle 16.29

\displaystyle 17.80

\displaystyle 18.19

Correct answer:

\displaystyle 17.14

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 19\sin B = 17.49

\displaystyle \sin B=0.92

\displaystyle B= 66.93

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

\displaystyle 61+66.93+C=180

\displaystyle C=52.07

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

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

\displaystyle d \sin 61= 14.99

\displaystyle d=17.14

 

Example Question #30 : Law Of Cosines And Sines

Find the length of the missing side, \displaystyle d.

12

Possible Answers:

\displaystyle 11.13

\displaystyle 13.22

\displaystyle 14.13

\displaystyle 15.92

Correct answer:

\displaystyle 14.13

Explanation:

First, use the Law of Sines to find the measurement of angle \displaystyle B.

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

\displaystyle 13\sin C = 8.09

\displaystyle \sin C=0.62

\displaystyle C= 38.32

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

\displaystyle 64+38.32+B=180

\displaystyle B=77.68

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

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

\displaystyle d \sin 64= 12.70

\displaystyle d=14.13

 

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