Question

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

Answer 1

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