Nathan's Blog

For this blog, I will show you the stuff from section 9-3, which involves the Law of Sines.

This is only with non-right triangles, and you only use it when you have an angle and opposite leg value you know.

Formula:

sin(angle)/opposite leg=sin(angle 2)/opposite leg 2
*Cross multiply to solve.

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.

Draw the triangle. You will find the missing angle by 180-110-20=50.

So, sin50/25=sin110/BC. 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

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

That's all for this blog. Just a little note here. The THETA symbol, is the lowercase y in the WEBDINGS font. Your Welcome.