Law of sines.

Last week, one of our lessons were Law of Sins
-You can only use Law of Sines in a non-right triangle when you have a pair, an angle and opposite side.

Formula:
sinA/a=sinB/b=sinC/c

Cross multiply to solve.

For inverses you get two answers which you then check to see if they work

Ex.1

ABC triangles:

angle C-25 degrees,side b-3,side c-2

First solve for angle B

Set up a proportion sin25/2 = sinB/3

cross multiply 3sin25/2 = 2sinB/2

SinB = -1(3sin25/2) = 39.34 degrees

Now that you have the angle measures to C and B, in order to find A you just subtract the sum of those two angles from 180 degrees.

For your second triangle,in order to find the degrees of angle B you have to make the one in the first triangle negetive and add 180.

After you do this,you will then be able to find your other angles.

To find the side lentgh of a you cross multiply

sin25/2 = sin115.66/a

cross multiply asin25/sin25 = 2sin115.66/sin25

a=4.265