Chapter 5: Trigonometric Functions Lessons 2 & 4: The Law of Cosines and The Law of Sines Mrs. Parziale

Finding Sides and Angles In the previous class, you used trigonometric ratios to find unknown sides or angles of right triangles. What happens if it is not a right triangle? If we know 2 sides and the included angle or 3 sides, then we use the Law of Cosines.

The Law of Cosines In any triangle ABC, The measures of angles and sides of any triangle can be found when we know 2 sides and the included angle or 3 sides by using the Law of Cosines.

Using the Law of Cosines to Find a Length Example 1: Find the missing side B A C

Using the Law of Cosines to Find an Angle Measure Example 2: A triangle has sides of length 4, 5, and 8.5. To the nearest degree, what is the measure of its largest angle?

Law of Sines The Law of Sines can be written in either of the following forms for  ABC with sides of lengths a, b, and c.

Example 3: Given  ABC below, m  A=28°, m  B=102°, and a=8. Find m  C, and lengths of sides b and c. 28° 102° 8 A B C b c

Example 4: You are making a door stopper from a block of wood. When the door rests against the stopper, you want the corner of the stopper to extend through the width of the door. If the bottom of the 2-inch wide door is.0.5 inches off the ground, what is the angle  of the door stopper? 2” 0.5” 

Closure State the Law of Cosines and Law of Sines When are each used? Problem: At a criminal trial, a witness gave the following testimony: –“The defendant was 20 ft from the victim. I was 50 ft from the defendant and 75 ft from the victim when the shooting occurred. I saw the whole thing.” –Use the Law of Cosines to show that the testimony has errors.