Question

law of cosines
the law of cosines is used to find 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
triangle image with vertices q, r, and another vertex, sides: qr=20, q(another vertex)=34, r(another vertex)=24
to the nearest whole degree, what is the measure of ∠q?
59°
44°
49°
54°

Explanation:

Step1: Solve for \(\cos Q\)

From the equation \(-980 = -1360\cos Q\), we can solve for \(\cos Q\) by dividing both sides by \(-1360\).
\(\cos Q=\frac{-980}{-1360}=\frac{980}{1360}=\frac{49}{68}\approx0.7206\)

Step2: Find the angle \(Q\)

To find the angle \(Q\), we take the inverse cosine (arccos) of \(0.7206\).
\(Q = \arccos(0.7206)\)
Using a calculator, \(\arccos(0.7206)\approx43.9^{\circ}\), which rounds to \(44^{\circ}\) when rounded to the nearest whole degree.

Answer:

\(44^{\circ}\) (corresponding to the option "44°")