Question

select the correct answer from each drop-down menu. consider the given triangles. note: figures not drawn to scale. the length of side pr in δpqr is 8.07 and the measure of ∠j in δjkl is drop - down menu with options 11.95, 35.30, 26.83, 63.16 °.

Explanation:

Step1: Calculate PR using Law of Cosines

In ΔPQR, sides PQ=5, QR=9, angle Q=63°.
Law of Cosines: $PR^2 = PQ^2 + QR^2 - 2(PQ)(QR)\cos(63°)$
$PR^2 = 5^2 + 9^2 - 2(5)(9)\cos(63°) ≈ 25 + 81 - 90×0.4540 ≈ 106 - 40.86 ≈ 65.14$
$PR ≈ \sqrt{65.14} ≈ 8.07$

Step2: Calculate ∠J using Law of Sines

In ΔJKL, sides JK=15, KL=11, angle L=52°.
Law of Sines: $\frac{JK}{\sin(L)} = \frac{KL}{\sin(J)}$
$\sin(J) = \frac{KL×\sin(L)}{JK} = \frac{11×\sin(52°)}{15} ≈ \frac{11×0.7880}{15} ≈ \frac{8.668}{15} ≈ 0.5779$
$∠J ≈ \arcsin(0.5779) ≈ 35.30°$

Answer:

Length of PR: 8.07; Measure of ∠J: 35.30°