Question

what is the measure of ∠p to the nearest whole degree? 35° 52° 57° 72° law of cosines: a² = b² + c² - 2bccos(a)

Explanation:

Step1: Identify sides for angle P

Opposite: QR=15; Adjacent: PR=14, PQ=17

Step2: Apply Law of Cosines

$15^2 = 14^2 + 17^2 - 2(14)(17)\cos(P)$

Step3: Calculate squares

$225 = 196 + 289 - 476\cos(P)$

Step4: Simplify equation

$225 = 485 - 476\cos(P)$

Step5: Solve for cos(P)

$\cos(P) = (485-225)/476 ≈ 0.5462$

Step6: Find angle P

$P ≈ \arccos(0.5462) ≈ 57^\circ$

Answer:

C. 57°