Question

in triangle qrs, what is the approximate measure of angle q? triangle image with sides: rs=32, sq=23, rq=21 options: a. 87.7° b. 93.2° c. 45.9° d. 96.9°

Explanation:

Step1: Identify sides for angle Q

Side opposite angle Q: RS = 32; adjacent: QS = 23; hypotenuse: RQ = 21? No, use Law of Cosines: $c^2=a^2+b^2-2ab\cos C$. For angle Q, sides adjacent: QS=23, QR=21; opposite: RS=32.

Step2: Apply Law of Cosines

$32^2 = 23^2 + 21^2 - 2(23)(21)\cos Q$
$1024 = 529 + 441 - 966\cos Q$
$1024 = 970 - 966\cos Q$
$54 = -966\cos Q$
$\cos Q = -\frac{54}{966} \approx -0.0559$

Step3: Calculate angle Q

$Q = \arccos(-0.0559) \approx 87.7^\circ$

Answer:

A. 87.7°