1. Warm up Notes Preliminary Activity Activity For Fun USING THE COSINE RULE TO FIND A MISSING ANGLE θ θ θ

2. Back 1. The cosine ratio is the ratio of A adjacentB oppositeC adjacent D opposite hypotenuse adjacent opposite hypotenuse 2. in the triangle sinθ is A 12B 9 9 12 C 9 D 12 15 3. Correct to four decimal places cos 53 o 18 ' is A 0.5976B 0.8018C 0.6018 D 1.3416 4. If tanθ = 7, then, to the nearest minute, θ = 5 A 54 o 27 ' B 54 o 28 ' C 16 o 22 ' D 16 o 23' 5. In the triangle, to the nearest minute, θ = A 38 o 29 ' B 38 o 30 ' C 38 o 3'D 51 o 30 ' 6. To one decimal place, x = A 20.5B 19.1 C 19.2D 15.0

3. Back The cosine rule is another method used to find the sides and angles in non-right-angled triangles. The cosine rule: In any triangle ABC, with sides and angles as shown a 2 = b 2 + c 2 - 2bccosA b 2 = a 2 + c 2 - 2accosB c 2 = a 2 + b 2 - 2abcosC The cosine rule is used to find ·the third side given two sides and the included angle ·an angle given three sides Rearranging a 2 = b 2 + c 2 - 2bccosA gives cosA = b 2 + c 2 - a 2 2bc which is a more convenient form for finding angles. Likewise, cosB = a 2 + c 2 - b 2 and cosC = a 2 + b 2 - c 2 2ac 2ab

4. Back Use the cosine rule to find θ correct to the nearest degree. cosA = b 2 + c 2 - a 2 2bc cosθ = 10.7 2 + 23.8 2 - 27.5 2 2 x 10.7 x 23.8 θ = 99 o (to the nearest degree)

5. Back 41.7% 56.3% 75.7% Complete exercise 5-07 Questions 1, 2, 4, 6, 8, 10, 12

6. Back $1 104 $1 096.50 $211.70 50.9% $17.25 8.5%

7. Back