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WarmUp: 1) Find the values of the six trigonometric functions for angle θ. A θ c b C o o a B 2) Solve ΔABC if A = 15 , C = 90 , and b = 8. Round measures of sides to the nearest tenth, and measures of angles to the nearest degree. Section 134: Law of Sines Write a formula for the area of the triangle below. A c B b h a C Suppose we dont know the height. What is a different expression representing the height? (Hint: Use the sine function). What is a new equation for the area of this triangle? Area Formula for a Triangle: A = 1 bc sin A 2 A = 1 ac sin B 2 A = 1 ab sin C 2 A b c B a C Examples: 1) Find the area of ΔABC to the nearest tenth. A 6 cm C All three area formulas represent the same area, so 1 bc sin A = 1 ac sin B = 1 ab sin C 2 2 2 Divide all three sides by 1/2 abc, what is left? o 25 B 3 cm The Law of Sines: In ΔABC, the ratio between the sine of any angle and its opposite side to the ratio between the sine of any other angle and its opposite side. sin A = sin B = sin C a b c C Examples: 2) Solve ΔABC. a B 100 o 9 53 o c A Homework: pg. 790791 #1222 even, 32, 34, 40, 41 Section 134 Vocab