How do you use the law of cosines or law of sines if you are given a = 4, b = 5, and c = 6?

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How do you use the law of cosines or law of sines if you are given a = 4, b = 5, and c = 6?

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Answer 1 · 2015-09-06T11:00:03

You can use the Law of Cosines to find the remaining angles.

Explanation:

If you mark angles as:
$A$ $A$ the angle opposite to side $a$ $a$
$B$ $B$ the angle opposite to side $b$ $b$
$C$ $C$ the angle opposite to side $c$ $c$

Then from the Law of Cosines you have:

$c^{2} = a^{2} + b^{2} - 2 a b cos C$ $c^2=a^2+b^2-2abcosC$

After substituting you get:

$6^{2} = 5^{2} + 4^{2} - 2 \cdot 5 \cdot 4 \cdot cos C$ $6^2=5^2+4^2-2*5*4*cosC$

$36 = 25 + 16 - 40 cos C$ $36=25+16-40cosC$

$40 cos C = 41 - 36$ $40cosC=41-36$

$cos C = \frac{1}{8}$ $cosC=1/8$

$C \approx 82.8 d e g$ $C~~82.8 deg$

If you repeat simmilar calculations for $B$ $B$ you get:

$cos B = \frac{9}{16}$ $cosB=9/16$

$B \approx 55.77 d e g$ $B~~55.77 deg$

Now you can calculate the remaining angle either using the Law of Cosies again or using the property of Sum of Angles in a Triangle

$A + B + C = 180$ $A+B+C=180$
$A = 180 - B - C$ $A=180-B-C$
$A = 180 - 55.77 - 82.8$ $A=180-55.77-82.8$
$A \approx 41.43 d e g$ $A~~41.43deg$

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How do you use the law of cosines or law of sines if you are given a = 4, b = 5, and c = 6?

1 Answer

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