Question

What is the measure of ∠P ? Round your answer to the nearest degree.

A.) 29°

B.) 42°

C.) 65°

D.) 78°

Answer 1

im lates but the answer on K12 is B. 42

Answer 2

Answer:

B. $42^{\circ}$

Step-by-step explanation:

We have been given an image of a triangle. We are asked to find the measure of angle P.

We will use law of sines to solve for angle P.

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$, where a, b and c are the sides corresponding to the angles A, B and C.

Upon substituting our given values we will get,

$\frac{sin(P)}{QR}=\frac{sin(Q)}{PR}$

$\frac{sin(P)}{47.6}=\frac{sin(73^{\circ})}{68}$

$\frac{sin(P)}{47.6}=\frac{0.956304755963}{68}$

$\frac{sin(P)}{47.6}=0.01406330523475$

$\frac{sin(P)}{47.6}\times 47.6=0.01406330523475\times 47.6$

$sin(P)=0.6694133291741$

Now we will use arcsin to find the measure of angle P.

$P=sin^{-1}(0.6694133291741)$

$P=42.021801403079^{\circ}\approx 42^{\circ}$

Therefore, the measure of angle P is 42 degrees and option B is the correct choice.