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WINSTONCH [101]
3 years ago
9

Solve the following triangle. Given A=51 degrees b=40 c=45

Mathematics
1 answer:
STALIN [3.7K]3 years ago
5 0

Answer:

a=36.87\ units

B=57.47^o

C=71.53^o

Step-by-step explanation:

step 1

Find the length side a

Applying the law of cosines

a^2=b^2+c^2-2(b)(c)cos(A)

substitute the given values

a^2=40^2+45^2-2(40)(45)cos(51^o)

a^2=1,359.4466

a=36.87\ units

step 2

Find the measure of angle B

Applying the law of sines

\frac{a}{sin(A)} =\frac{b}{sin(B)}

substitute the given values

\frac{36.87}{sin(51^o)} =\frac{40}{sin(B)}

sin(B)=\frac{sin(51^o)}{36.87}{40}

B=sin^{-1}(\frac{sin(51^o)}{36.87}{40})=57.47^o

step 3

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

substitute the given values

51^o+57.47^o+C=180^o

108.47^o+C=180^o

C=180^o-108.47^o=71.53^o

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