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Precalculus : The Ambiguous Case (SSA, ASS)

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Example Question #1 : The Ambiguous Case (Ssa, Ass)

Triangle_700

Given b=4ft, c=6ft, and $B=36^\circ$ , what is the measurement of to the nearest degree?

Possible Answers:

$82.2^\circ$

$82.15^\circ$

$82^\circ$

$83^\circ$

Correct answer:

$82^\circ$

Explanation:

Using the information we have, we can solve for $\angle C$ :

$\frac{sinB}{b}=\frac{sinC}{c}$ .

Plugging in what we know, we have:

$\frac{sin(36)}{4}=\frac{sinC}{6}$ .

Then, solve for sinC :

$6\cdot\frac{sin(36)}{4}=sinC$ .

Simplify, then solve for : 0.8816778784=sinC which means $sin^{-1}(.8816778784)=C$ .

Therefore, after rounding to the nearest degree, $C=62^\circ$ .

To solve for $\angle A$ , subtract $\angle B$ and $\angle C$ from $180^\circ$ : $180^\circ-36^\circ-62^\circ=82^\circ$ .

Therefore, $\angle A = 82^\circ$ .

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Example Question #1 : Law Of Sines

Find the length of the missing side, .

Possible Answers:

29.01

22.36

24.51

26.77

Correct answer:

22.36

Explanation:

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

$\frac{15}{\sin 41}=\frac{20}{\sin B}$

$15\sin B = 13.12$

$\sin B=0.87$

B= 61.01

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

41+61.01+A=180

A=77.99

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

$\frac{d}{\sin 77.99}=\frac{15}{\sin 41}$

$d \sin 41= 14.67$

d=22.36

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Example Question #21 : Trigonometric Applications

Find the length of the missing side, .

Possible Answers:

29.12

25.53

28.54

20.57

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

10.73

9.89

8.14

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 #5 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

13.98

15.12

12.37

14.63

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

8.81

7.84

8.95

9.51

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

14.12

15.62

11.71

19.35

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

27.98

20.18

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

31.50

24.12

35.91

29.07

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 #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

10.25

7.64

9.92

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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Precalculus : The Ambiguous Case (SSA, ASS)

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : Law Of Sines

Example Question #21 : Trigonometric Applications

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #5 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

All Precalculus Resources

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