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Chapter 9

# Chapter 9 - Chapter9.1: , (acute,rightorobtuse...

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Chapter 9.1: The law of sines and cosines In this section we will discuss two laws, the law of sines and cosines that establishes relationship between the sides and angels in any triangle (acute, right or obtuse triangles) . The purpose of these laws is to solve a triangle (find out the lengths of the three sides and the measurements of the three angels) when you know only some of the side lengths or some of the angel measurements. You will have to decide which of the laws is better to use given the provided information in the question. The Law of sines: In any triangle, the ratio of the sine of an angle to the lengths of the opposite side is constant. sin A a = sin B b = sin C c Proof:

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Note: To use law of sines, you will need the measure of one angel and its opposite side plus another angel or side. Ex: Suppose a=4cm, b=9cm and <B=60 0 . Find the angels <A, <C, and side c
Ex: Given < C = 45 0 , b = 4 2 ft , c = 8ft . Solve the triangel. Note: Is it possible for this triangle to have two solutions?

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Ex: Find the lengths a, b, c, and d in the following figure
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Chapter 9 - Chapter9.1: , (acute,rightorobtuse...

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