Trigonometry: Using the law of Sines and Cosine Formulas
This is a free lesson from our course in Trigonometry
 
   
In this lesson you'll learn how to solve problems in which the law of sines and the law of cosines are used. You will learn it with the help of some examples, practice questions with solution and using video explanations by the instructor that brings in an element of real-class room experience. The Laws of Sines and Cosines play fundamental roles in solving oblique triangles by determining the unknown parts of a triangle. These unknown parts consist of either sides or angles of a triangle. When solving for unknown angles and/or sides, it is important to determine the appropriate law to use and put it in the given information. The given information is used to determine the equation. (More text below video...)
<h2>Trigonometry - Using the law of Sines and Cosine Formulas</h2> <p>angle, triangle, laws of sines and cosines, video, measure, right triangles, sides, oblique triangles, examples, solutions, sine, cosine, trigonometric functions, solving triangle, right triangles, laws of sine, laws of cosine, math help, practice questions, quizzes</p> <p>The Laws of Sines and Cosines play fundamental roles in solving oblique triangles by determining the unknown parts of a triangle. These unknown parts consist of either sides or angles of a triangle. When solving for unknown angles and/or sides, it is important to determine the appropriate law to use and put it in the given information. The given information is used to determine the equation.</p>
Other useful lessons:
Definitions - Law of Sines & Cosines
The Ambiguous Case
Area of a Triangle

(Continued from above) If any two angles and the measure of one side or any two sides and one angle of a triangle are given, the measure of the remaining sides and angles of the triangle can be determined by using the laws of sine or the laws of cosine

For example: given triangle ABC, where mA = 28, b = 5 and mC = 91. To find the measure of side c first sketch the triangle, then by using the triangle-angle-sum theorem, you can easily work out measure of B = 61. Now using the law of sines i.e., sin B/b = sin C/c and plugging in the corresponding known values, you'll get the answer rounded off to the nearest tenth c = 5.7.

A Cosine Law example :
You have given two sides of the triangle and an angle, say
b = 12, c = 10 and A = 50
and you have to find out the length of the third side.
In this case you can use the cosine formula as
a = b + c - 2bc cos A
a = 12 + 10 2(12)(10) cos 50
a = 144 + 100 240(0.0642)
a = 89.92
a= 9.48
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