Help solve the triangle?

Question

Angle A = 22 degrees

Angle B and C = Unknown

a = 6

b = 4

c = unknown

Answer 1

You can solve this using The Law of Sines:

 

a / sin(A)  =  b / sin(B)      [and also = c / sin(C)  ]

 

cross-multiplying around the = sign gives:

 

a sin(B) = b sin(A)

 

so

 

sin(B) = (b/a) sin(A)

 

and then

 

B = arcsin[  (b/a) sin(A)  ]     also written as:

   =  sin^-1 [ (b/a) sin(A) ]

 

Putting in your numbers and using a calculator will give B, be sure it is in degrees.

 

Then A+B+C=180 because it is a triangle, so you can figure out C.

 

Finally use the law of sines again (with c / sin(C) ) to find c .

 

I hope this helps enough.