Question

Solve the triangle A=21 C=105 c=5

Answer 1

Granted that uppercase letters are the angles measurements and lowercase letters are the side lengths. I also was unable to round as I don't know to what decimal you need to round to.

First to find the measure of angle B, we must subtract A and C from 180

`180-21-105=54`

B=54

Next, we can use the law of sines in order to find the measures of a and b

As a reminder, The law of sines is

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

First, lets solve for b

`(b)/(sin54)=(5)/(sin105) \\\\b=((5)sin54)/(sin105)\\\\b=4.187780119`

Next lets solve for a

`(a)/(sin21)=(5)/(sin105) \\\\a=((5)sin21)/(sin105)\\\\a=1.85504901`