Nathan's Blog

For this blog, I will be going over section 9-3 and 9-4, which deals with the Law of Sines and the Law of Cosines.
Law of Sines:
-Only used with non-right triangles.
-Only use 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=25m, angle A=110 degrees and angle B=20 degrees. Find AC and BC.

sin50/25=sin110/BC
BC=25sin110/sin50
BC=30.667 m

sin50/25=sin20/AC
AC=25sin20/sin50
AC=11.162 m

Law of Cosines:
-Used when you don't have a pair in a non-right triangle.

Ex. Suppose that two sides of a triangle have lengths of 3 cm and 7 cm and that the angle between them measures 130 degrees. Find the third side of the triangle using the Law of Cosines.

p^2=3^2+7^2-2(3)(7)cos130
p=√3^2+7^2-2(3)(7)cos130
p=9.22 cm