Question

Calculate cos theta to two decimal places.

A. 0.69
B. 1.38
C. -0.07
D. 0.77

Answer 1

A. 0.69

Explanation:

Using the cosine law

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

8² = 7² + 11² - 2 × 7× 11 cos ∅

64 = 49 + 121 -154 × cos ∅

64 = 170 - 154 cos ∅

64 - 170 = -154 cos ∅

- 106 = -154 cos ∅

cos ∅ = -106/-154

cos ∅ = 0.6883116883 ≈ 0.69

Answer 2

A. 0.69

Explanation:

We need to use cosine theorem:

c²=a²+b² - 2ab* cos(θ)

c=8, a=7, b=11

8² = 7²+11² - 2*7*11 *cos(θ)

64 = 49 + 121 - 154*cos(θ)

64 - 170 = - 154*cos(θ)

- 106/ (- 154) = cos(θ)

cos(θ) = 0.69