Question 455003: How can we find the length of one side of a triangle when two sides and an angle is given using sin and cos?Please give an example.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How can we find the length of one side of a triangle when two sides and an angle is given using sin and cos?Please give an example.
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When two sides and the included angle are given, use the Law of Cosines to find the third side.
When two sides and not the included angle are given, use the Law of Sines to find a second angle. Knowing two angles, you can always find the third. After this you can use the Law of Sines or Cosines to find the third side.
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Example:
Draw a triangle labeled A,B,C (clockwise), with corresponding sides a,b,c opposite these angles.
Say, sides b & c and the included angle A are given. Side a would be calculated directly by using the Law of Cosines as follows: a^2=b^2+c^2-2*b*c Cos A.
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Say, sides b & c and the angle B are given. First, we need to find a second angle by using the Law of Sines as follows: sin B/b=Sin C/c, Sin C=(c/b)sin B. After you find C, you can easily find A, after which you can use either Law of Sines or Cosines to find the third side.
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