Question

question 3 of 10
calculate cosθ to two decimal places.
7
11
8
a. 0.69
b. -0.07
c. 0.77
d. 1.38

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). Here, we can label the sides: let \(a = 7\), \(b = 11\), and \(c = 8\). Rearranging the Law of Cosines to solve for \(\cos\theta\), we get \(\cos\theta=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).

Step2: Substitute the values

Substitute \(a = 7\), \(b = 11\), and \(c = 8\) into the formula:

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Answer:

A. 0.69