Trig Angles Question

Question

In triangle ABC, B=120 degrees, C = 10 degrees and c=29 inches. find b.

Apply the rules regarding the use of significant digits

Answer 1

There is a property called Law of Sines  that says

A/sina = B/sinb = C/sinc    Note: a/sina means ( Side A is divided by sin(a) where small a is the degrees) 

 

Since we do not have valies for A or a we must use B/sinb = C/sinc because the questions privides 3 of the 4 values ( it provides us with C= 29inches  c= 10 degrees and b= 120 degrees.)

 

Plugging the values in gives us.

 

B/sin120 = 29/sin10

B/0.86602540378 =167.004344011 (solved for sin 120 and 29/sin10)

B= 144.630004456 inches (multiplies .8602540378)

B= 144.63

 

Hope this helps!

Answer 2

Using the law of sines: 

 

b/sin(B)=c/sin(C), or

 

b=29*sin(120^o)/sin(10^o).

 

Hope that helps.