Word Problems: Law of Sines 
In order to solve problems which require the application of the Law of Sines, it is necessary to A typical problem requiring the Law of Sines in order to solve it involves a triangle in which there is no right angle. We are given some information about a triangle, but we have to find measurements of other sides and/or angles. The Law of Sines for a triangle ABC is stated below, assuming that the side opposite angle A is a, the side opposite angle B is b, and the side opposite angle C is c: Suppose in triangle ABC that are given. Find the measure of side c. This would be a typical example of this type of problem.
First, we make a diagram. A diagram of this triangle is shown below.
In this diagram the given distances and angles are labeled:
The variable c is chosen to represent the unknown measurement of the side opposite angle C. This is the object of the question.
To relate the known measurements and the variable, an equation is written. In this case the equation involves the ratios of the sines of angles to the opposite sides. We have
We now need to know the measure of angle B to solve the problem.
The sum of angles A and C is 28º + 91º = 119º. Since the sum of the angles in a triangle equals 180º we know that angle B must have a measure of
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As you can see, this type of problem requires a diagram of a carefully labeled triangle. The measurements of a side and two angles should be labeled based on the information given. One measurement of a side in the triangle is missing. It is the goal of the problem to find this measurement. First you should assign a variable to represent the missing measurement. We usually use a lower case English letter to represent the measure of a side of the triangle. Use of the Law of Sines involves a simple equation. It is important to set a calculator for degrees if that is the manner in which the angles are measured. If one angle and two sides are known, it is best to use the Law of Cosines to find the measurements of missing parts of the triangle.

M Ransom


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