Name: ___________________________ Date: __________________________

MCF3M: Cosine Law

	Please remember that the Cosine Law is used to solve triangles where you are given 
-	all three sides
-	two sides and the enclosed angle

For any triangle ABC, the cosine law is
	c² = a² + b² - 2ab cos C

Please remember that these work for any acute triangle (not just right angle triangles).

Example 1: Use the cosine Law to find x

First, sine law cannot be used in this triangle, because we only have one angle and are looking for the third side.  The Pythagorean theorem cannot be used because this isn’t a right triangle.  So we have to use the cosine law.

x² = (5)² + (6)² - 2(5)(6)cos 48°

	Please remember your order of operations.  The five squared is added to the six squared which then negative 2 times 5 times 6 times cos 48 is subtracted….watch.
			
	Please try this on your calculator to make sure that you can get the answer.

Example 2: Use cosine Law to find θ

	We have to use cosine law because there are no angles to relate (as in sine law).  We cannot use soh cah toa because there are no right angles.

	The difficulty is to find what side is by itself on the left hand side.  It will be the 29, because it is opposite theta.
		CONTINUED ON NEXT PAGE

				

Practice
1)	In ∆CAT, c = 6.4m, a = 4.0m, and <T = 65°.  How long is side t?
2)	In ∆ABC, <A = 48°, c = 15m and b = 12m.  Solve the triangle
3)	An isosceles triangle has sides of 8cm, 12cm and 12cm.  Find the measures of the base sides.
4)	Two airplanes leave an airport at the same time.  One travels at 355km/h and the other at 450km/h.  Two hours later they are 800km apart.  Find the angle between their courses.
5)	Jason is flying a kite and let out the entire 150m ball of kite string.  He notices that the string forms a 70° angle with the ground.  Luke is on the other side of the kite and sights the kite at an angle of elevation (from the ground) of 30°.  How far is Luke from Jason?
6)	Solve the triangle ABC if a = 6.8, b = 5.7, c = 6.5.