Calculate cos theta to two decimal places. A. 0.69 B. 1.38 C. -0.07 D. 0.77

Answer:

A. 0.69

Step-by-step explanation:

Using the cosine law, we have:

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

Applying it: 8² = 7² + 11² - 2 × 7 × 11 cos ∅

64 = 49 + 121 - 154 × cos ∅

64 = 170 - 154 cos ∅

64 - 170 = -154 cos ∅

- 106 = -154 cos ∅

therefore, cos ∅ = -106/-154

so, cos ∅ approximates to 0.69

Answer:

c²=a²+b² - 2ab * cos(θ)

where c=8, a=7, b=11

Thus, 8² = 7² + 11² - 2*7*11 *cos(θ)

64 = 49 + 121 - 154*cos(θ)

Thus, 64 - 170 = - 154*cos(θ)

- 106/(- 154) = cos(θ)