In this blog I will be explaining section 9-3 which explains the law of sines.

-First it is only used with non-right triangles.

- only use when you have an angle and opp leg value you know.

Formulas:

- sin(angle)/opp leg = sin (angle2)/opp leg 2

- then you just cross multiply

Ex.Ex. A civil engineer wants to determine the distance from points A and B to an inaccessible point C. From direct measurement, the engineer knows that AB=25 m; angle A=110 degrees and angle B=20 degrees. Find AC and BC.

First you have to draw the triangle,then you will find the missing angle by subtracting 180-110-20=50.

sin50/25=sin110/BC then you cross multiply to get:BC=25sin110/sin50
BC=30.667 m

Now to find AC: sin50/25=sin20/AC
AC=25sin20/sin50
AC=11.162 m

Ex 2. In triangle RST, angle S=126 degrees, s=12, t=7. Determine whether angle T exists. If so, find all possible measures of angle T.

sin126/12=sinT/7
T=sin-1(7sin126/12)
T=28.159 degrees

Now you must find another angle. Sin is related to Y and is positive in Q I and II.
-28.159+180=151.841

Then you test the angles in the triangle. 151.841 + 126 exceeds 180. So the only angle that can work, is 28.159.