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igomit [66]
3 years ago
12

Use the Law of Sines to solve the triangle. Round your answers to two decimal places.

Mathematics
1 answer:
mario62 [17]3 years ago
8 0

Answer:

Step-by-step explanation:

The Law of Sines is

\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}

Filling in what we are given:

\frac{sin(110.8)}{25.3}=\frac{sin(18.2)}{c}

Cross multiply to get

csin(110.8)=25.3sin(18.2) and divide to solve for side c:

c=\frac{25.3sin(18.2)}{sin(110.8)} which gives you that

c = 8.45

We know that angle B has to be the difference between 180  and angle A and angle C, so

angle B = 51

Now we can solve for side b:

\frac{sin(110.8)}{25.3}=\frac{sin(51)}{b} and

b=\frac{25.3sin(51)}{sin(110.8)} and

b = 21.03

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