Question

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

A = 110.8°, C = 18.2°, a = 25.3

Answer 1

Explanation:

The Law of Sines is

`(sinA)/(a)=(sinB)/(b)=(sinC)/(c)`

Filling in what we are given:

`(sin(110.8))/(25.3)=(sin(18.2))/(c)`

Cross multiply to get

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

`c=(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:

`(sin(110.8))/(25.3)=(sin(51))/(b)` and

`b=(25.3sin(51))/(sin(110.8))` and

b = 21.03