Answer:
B. [tex]42^{\circ}[/tex]
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.
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex], where a, b and c are the sides corresponding to the angles A, B and C.
Upon substituting our given values we will get,
[tex]\frac{sin(P)}{QR}=\frac{sin(Q)}{PR}[/tex]
[tex]\frac{sin(P)}{47.6}=\frac{sin(73^{\circ})}{68}[/tex]
[tex]\frac{sin(P)}{47.6}=\frac{0.956304755963}{68}[/tex]
[tex]\frac{sin(P)}{47.6}=0.01406330523475[/tex]
[tex]\frac{sin(P)}{47.6}\times 47.6=0.01406330523475\times 47.6[/tex]
[tex]sin(P)=0.6694133291741[/tex]
Now we will use arcsin to find the measure of angle P.
[tex]P=sin^{-1}(0.6694133291741)[/tex]
[tex]P=42.021801403079^{\circ}\approx 42^{\circ}[/tex]
Therefore, the measure of angle P is 42 degrees and option B is the correct choice.
