In triangle ABC, AB=5, BC=3, and ?BAC=20°. Find all possible...

Question

In triangle ABC, AB=5, BC=3, and ∠BAC=20°. Find all possible values of ∠C.

Answer 1

Hey Mike,

 

You can use Laws of Sines for this problem:

 

 

sin (20) / 3 = sin C / 5

 

If you calculate this, sin C = [5 sin (20)] / 3

 

And sin C comes out to be 0.5700335722.  As you take sin^-1 of this, you will get 34.75 degrees. 

 

Since sine is "+" in 1st and 2nd quadrants, there will be 2nd possible angle: 180 - 34.75 = 145.25 degrees.  [You have to subtract from 180 because it will be -34.75 degrees and it measures from x-axis in unit circle (if you remember)].

 

So, your answers are 34.75 degrees & 145.25 degrees for angle C

 

So, possibilities are 34.75 degrees or 145.25 degrees.  Herei is an example image of it:

 

 

 

 

 

From that, here are 2 possible triangles:

20 - 34.75 - 125.25   &   20 - 145.25 - 14.75

 

Good luck to you.