Question

question 5 of 10 select the angle that correctly completes the law of cosines for this triangle. 5² + 13² - 2(5)(13)cos ___ = 12² a. 67° b. 90° c. 180° d. 23°

Explanation:

Step1: Recall law of cosines formula

The law of cosines for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). In the equation \(5^{2}+13^{2}-2(5)(13)\cos\theta = 12^{2}\), the side opposite to the angle \(\theta\) is \(12\).

Step2: Identify the angle

In the given right - triangle, the angle opposite to the side of length \(12\) is \(23^{\circ}\).

Answer:

D. \(23^{\circ}\)