You can use the law of cosine to find the measure of angle P.
The measure of angle P is given by
Option C : 57°
What is law of cosine?
Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]c^2 = a^2 + b^2 - 2ab\cos(\theta)}[/tex]
(c is opposite side to angle A)
Using the law of sines to find the measure of angle P in the given context
Refer to the attached figure below.
Using the cosine law, we get
|PQ| = a = 17 units, |QR| =length of opposite side to P = c = 15 units, |PQ| = b = 14 units.
Thus, let angle QPR be of θ degrees, then
[tex]cos(\theta) =\dfrac{a^2 + b^2 - c^2}{2ab} = 0.546\\\\\theta = arccos(0.546) = 56.9^\circ, -56.9^\circ[/tex]
triangle's angles are measured positive, thus, measure of angle P came out as 56.9 degrees or approx 57°
Thus,
The measure of angle P is given by
Option C : 57°
Learn more about law of cosine here:
https://brainly.com/question/17289163
