Question

calculate \\( cos \theta \\) to two decimal places.

a. -0.07

b. -0.42

c. -0.14

d. 0.69

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). Let \(a = 7\), \(b = 8\), \(c = 11\). Then \(11^{2}=7^{2}+8^{2}-2\times7\times8\times\cos\theta\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(\cos\theta\)

\(\cos\theta=\frac{8}{-112}\approx - 0.07\)

Answer:

A. -0.07