Warm up Notes Preliminary Activity Activity For Fun

USING THE COSINE RULE TO FIND A MISSING ANGLE

θ

θθ

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1. The cosine ratio is the ratio of A adjacent B opposite C adjacent

D opposite hypotenuse adjacent opposite

hypotenuse

2. in the triangle sinθ isA 12 B 9 9 12C 9 D 12 15 15

3. Correct to four decimal places cos 53o 18' isA 0.5976 B 0.8018 C 0.6018

D 1.3416

4. If tanθ = 7 , then, to the nearest minute, θ = 5

A 54o27' B 54o28' C 16o22'

D 16o23'

5. In the triangle, to the nearest minute, θ =A 38o29' B 38o30'

C 38o3' D 51o30'

6. To one decimal place, x = A 20.5 B 19.1C 19.2 D 15.0

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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

a2 = b2 + c2 - 2bccosAb2 = a2 + c2 - 2accosBc2 = a2 + b2 - 2abcosC

The cosine rule is used to find·the third side given two sides and the included angle·an angle given three sides

Rearranging a2 = b2 + c2 - 2bccosA gives cosA = b2 + c2 - a2

2bcwhich is a more convenient form for finding angles.

Likewise, cosB = a2 + c2 - b2 and cosC = a2 + b2 - c2

2ac 2ab

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Use the cosine rule to find θ correct to the nearest degree.

cosA = b2 + c2 - a2

2bc

cosθ = 10.72 + 23.82 - 27.52

2 x 10.7 x 23.8θ = 99o (to the nearest

degree)

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41.7%

56.3%

75.7%

Complete exercise 5-07

Questions 1, 2, 4, 6, 8, 10, 12

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$1 104

$1 096.50

$211.70

50.9%

$17.25

8.5%

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