Option B:
Law of cosine, two sides and the included angle are known.
Solution:
Let us first know the law of cosines and law of sines.
Law of cosine:
If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.
[tex]c^2=a^2+b^2-2abcos\theta[/tex]
Law of sine:
The sides of a triangle are to one another in the same ratio as the sines of their opposite angles.
[tex]$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Given ∠P and the sides r, q are known.
To find the value of p:
Option A: Law of cosines, all sides are known.
It is false by the above definition of law of cosine.
Option B: Law of cosine, two sides and the included angle are known.
It is true by the above definition of law of cosine.
Option C: Law of sines, all sides are known.
It is false, because one angle is given in question.
Option D: Law of sines, two angles and the included side are known.
It is false, because two angles are not given.
Option B is the correct answer.
Hence the answer is "Law of cosine, two sides and the included angle are known".
