Use the Law of Sines to solve for each side length or angle

Use the Law of Sines to solve for each side length or angle measure. Find side length c. Find m A. Solve the triangle below. First, find m B. Use the Law of Sines to find side lengths a use the Law of Sines to find side length c.

Solution

m<B= 180-(m<A +m<B)= 180-(70+75)= 35

using sin law we get

Sin B/b= sin A/a

sin 35/3.1=sin 70/a

a= 3.1 sin 70/sin 35

a=5.08

Sin B=b=Sin C/c

sin 35/3.1= sin 75/c

c= 3.1 sin 75/sin 35

c=5.2