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

B.
`42^(\circ)`

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.

`(sin(A))/(a)=(sin(B))/(b)=(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,

`(sin(P))/(QR)=(sin(Q))/(PR)`

`(sin(P))/(47.6)=(sin(73^(\circ)))/(68)`

`(sin(P))/(47.6)=(0.956304755963)/(68)`

`(sin(P))/(47.6)=0.01406330523475`

`(sin(P))/(47.6)* 47.6=0.01406330523475* 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.