Question

what is the measure of ∠s to the nearest whole degree? 19° 26° 30° 33° law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Identify sides for angle S

Opposite: QR=10; Adjacent: SQ=17, SR=18

Step2: Apply Law of Cosines

$10^2 = 17^2 + 18^2 - 2(17)(18)\cos(S)$

Step3: Solve for cos(S)

$\cos(S) = (17^2 + 18^2 - 10^2)/(2×17×18) = 513/612 ≈ 0.838$

Step4: Find angle S

$\angle S = \arccos(0.838) ≈ 33^\circ$

Answer:

D. 33°