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...)
(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
a² = b² + c² - 2bc cos A
a² = 12² + 10² – 2(12)(10) cos 50°
a² = 144 + 100 – 240(0.0642)
a² = 89.92
a= 9.48
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A
= 28
, b =
5 and m