How do you use the law of cosines or law of sines if you are given A= 70 Degrees B= 80 Degrees, a=9?

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How do you use the law of cosines or law of sines if you are given A= 70 Degrees B= 80 Degrees, a=9?

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Answer 1 · 2015-06-02T08:50:58

You can use the law of sines to calculate the remaining sides of the triangle:

The law of sines says that in every triangle :
$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/sinA=b/sinB=c/sinC$ ,

where $A, B, C$ $A,B,C$ are angles,

$a, b, c$ $a,b,c$ are sides opposite to respective angles.

In this case you can calculate remeining sides using the law of sines.

First you can calculate the remaining angle, because the sum of angles in every triangle is 180 degrees, so:

$70 + 80 + C = 180$ $70+80+C=180$
$150 + C = 180$ $150+C=180$
$C = 30$ $C=30$

Now you can use the law of sines to calculate $c$ $c$

$\frac{a}{sin 70} = \frac{c}{sin 30}$ $a/sin70=c/sin30$

$\frac{9}{0.94} = \frac{c}{0.5}$ $9/0.94=c/0.5$

$0.94 c = 4.5$ $0.94c=4.5$

$c \approx 4.8$ $c~~4.8$

Now you can use the law of sines again to calculate $b$ $b$

$\frac{b}{sin 80} = \frac{c}{sin 30}$ $b/sin80=c/sin30$

$\frac{b}{0.98} = \frac{4.8}{0.5}$ $b/0.98=4.8/0.5$

$\frac{b}{0.98} = 9.6$ $b/0.98=9.6$

$b \approx 9.4$ $b~~9.4$

So now you can write the answer:

$A = 70, B = 80, C = 30$ $A=70,B=80,C=30$
$a = 9, b \approx 9.4, c \approx 4.8$ $a=9,b~~9.4,c~~4.8$

$B and C$ $B and C$ can only be calculated approximately, because $sin 70$ $sin70$ and $sin 80$ $sin80$ don't have exact rational values. I used the approximation to 2 decimal places.

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How do you use the law of cosines or law of sines if you are given A= 70 Degrees B= 80 Degrees, a=9?

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