Law of Sines

Question

Given the triangle ABC with angles A= 58°, B=70°, and side c=21cm. Using the Law of Sines, find the length of the side a. Approximate your answer to the nearest whole number.

 

Show all step by step work to the solution of the problem. Also give the final solution. Please and Thank You.

Answer 1

Angle A is opposite to side BC.  BC is side a.

Angle B is opposite to side AC.  AC is side b.

Angle C is opposite to side AB.  AB is side c.

 

Using the law of sines,

 

sinA / BC = sinC / AB

 

 

Solve for BC.

 

BCsinC = ABsinA

 

BC = ABsinA / sinC

 

a = c(sinA) / [sin(180 - A - B)]

 

 

Plug in the value of c, A, and B into the bolded equation.