1. 8-7 Law of Cosines
Law of Cosines: Allows us to solve a triangle when the Law of Sines cannot be used.
Theorem 8.9: Let ∆ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with measures A, B, and C, respectively. Then A B C a b c

2. Example 1
In ∆DEF, e = 19, f = 28, and m∠D = 49. Find d.

3. Example 2
In ∆TVW, v = 18, t = 24, and w = 30. Find m∠W.

4. Concept Summary To Solve Given Begin by using Right Triangle Two legs
Tangent
Leg and hypotenuse
Sine or cosine
Angle and hypotenuse
Angle and a leg
Sine, cosine, or tangent
Any Triangle
Two angles and any side
Law of Sines
Two sides and the angle opposite one of them
Two sides and the included angle
Law of Cosines
Three sides

5. Example 3
Solve ∆XYZ for x = 10, y = 11, and z = 12.

6. Example 4 Refer to the picture on p. 482
An architect is designing a playground in the shape of a quadrilateral. Find the perimeter of the playground to the nearest tenth.
1) Use Pythagorean Theorem to find JL
JL = 22.2
2) Use Law of Cosines (JL, KJ, ∠LJK) to find KL.
KL = 12.4
Answer: m

7. Homework #55
p even, 16-22, odd, 41, 43-44