Question

the law of cosines is used to find the measure of ∠q. to the nearest whole degree, what is the measure of ∠q? 24² = 20² + 34² - 2(20)(34)cos(q) 576 = 400 + 1156 - (1360)cos(q) 576 = 1556 - (1360)cos(q) -980 = - (1360)cos(q) options: 44° 49° 54° 59°

Explanation:

Step1: Solve for \(\cos(Q)\)

From \(-980=-1360\cos(Q)\), we get \(\cos(Q)=\frac{980}{1360}\approx0.7206\)

Step2: Find \(Q\)

Using the inverse - cosine function \(Q = \cos^{-1}(0.7206)\)

Answer:

\(44^{\circ}\)