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Law of Cosines

Law of Cosines. Section 12-3.

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Law of Cosines

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  1. Law of Cosines Section 12-3

  2. The Law of Sines enabled you to find the lengths of sides of a triangle or the measures of the angles in certain situations. To use the Law of Sines, you needed to know the measures of two angles and the length of any side, or the lengths of two sides and the measure of the angle opposite one of the sides. What if you know a different combination of sides and angles?

  3. Two hot-air balloons approach a landing field. One is 12 m from the landing point and the other is 17 m from the landing point. The angle between the balloons is 70°. How far apart are the two balloons?

  4. Sketch one altitude to form two right triangles, so that one of the right triangles contains the 70° angle.

  5. Sketch one altitude to form two right triangles, so that one of the right triangles contains the 70° angle.

  6. Around the Corner • The towns of Easton and Westville lie on opposite sides of a mountain. The townspeople wish to have a tunnel connecting the towns constructed through the mountain. A construction engineer positions herself so that she can see both towns. She plans to make some measurements and use trigonometry to determine the length of the proposed tunnel.

  7. In this investigation you will simulate this situation. Position three members of your group so that two people are on opposite sides of a wall and the third person can see both of them. The first two group members represent the two towns, and the wall represents the mountain. The third member represents the engineer. Find the distance between the two towns. Sketch an overhead view of the situation, show the measurements you make, and show your calculations.

  8. Example B • Find the unknown angle measures and side lengths.

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