Warm Up 1) Find the height of the triangle below: 2) Find the area of the triangle below: A B C 10 15 8 20º 32 130.8°

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Presentation transcript:

Warm Up 1) Find the height of the triangle below: 2) Find the area of the triangle below: A B C º °

9.2: Area of a Triangle

9.2 Area of a Triangle Objectives: 1.Find the area of a non-right triangle. Vocabulary: base, altitude, area, parallelogram, quadrilateral

The area A of a triangle equals one-half the product of two of its sides times the sine of its included angle. A = ½ absin(C) A = ½ acsin(B) A = ½ bcsin(A)

Find the area of the quadrilateral. A B C D 130º

9.4: Law of Cosines

8 Deriving the Law of Cosines Write an equation using Pythagorean theorem for shaded triangle. b h a k c - k ABAB C c

Note:  capital letters always stand for __________!  lower-case letters always stand for ________! When to use the Law of Cosines:  SSS  SAS angles sides A B C a b c The Law of Cosines!

Let’s do some problems! Ex. 1: Use the Law of Cosines to solve each triangle. Round any decimal answers to the nearest tenth. a ˚ B C A 19 a 57.3˚

b. E R D ˚ 108.2˚

T A C c 40˚ 53.0˚ Now you try!

Exit Slip Solve the triangle: p = 3, q = 8, <R = 50˚