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Precalculus : Use the laws of cosines and sines

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Example Questions

Example Question #31 : Use The Laws Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

8.10

6.91

5.92

6.37

Correct answer:

6.37

Explanation:

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

$\frac{5}{\sin 50}=\frac{3}{\sin C}$

$5\sin C = 2.30$

$\sin C=0.46$

C= 27.39

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

50+27.39+B=180

B=102.61

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

$\frac{d}{\sin 102.61}=\frac{5}{\sin 50}$

$d \sin 50= 4.88$

d=6.37

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Example Question #32 : Use The Laws Of Cosines And Sines

What is the largest possible angle, measured in degrees, in triangle ABC if $\angle A = 30^\circ$ , AB = 10 , and BC = 6 ?

Possible Answers:

$107.56^\circ$

$144.56^\circ$

$156.56^\circ$

$123.56^\circ$

$93.56^\circ$

Correct answer:

$123.56^\circ$

Explanation:

In the ambiguous SSA case, use Law of Sines to solve for the angle opposite the given side.

$\\* \frac {\sin A}{a} = \frac {\sin C}{c} \\* \\* \frac {\sin 30^\circ}{6} = \frac {\sin C}{10} \\* \\* C = \arcsin \left(\frac {10 \sin 30^\circ}{6}\right) \approx 56.44^\circ$

If $C = 56.44^\circ$ , then $B = 93.56^\circ$ .

However! Another possible value of C is $(180 - 56.44)^\circ = 123.56^\circ$ .

In this case the angles will be $30^\circ, 123.56^\circ, 26.44^\circ$ .

This is bigger than $93.56^\circ$ and is consequently the answer.

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Precalculus : Use the laws of cosines and sines

Study concepts, example questions & explanations for Precalculus

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Example Question #31 : Use The Laws Of Cosines And Sines

Example Question #32 : Use The Laws Of Cosines And Sines

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