Question

Question 6(Multiple Choice Worth 3 points)(05.04 LC)triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle RIf ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q. Law of Sines, two sides and an opposite angle are known Law of Sines, two angles and the included side are known Law of Cosines, all sides are known Law of Cosines, two sides and the included angle are known

Answer 1

1)If ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.

We have the law of sin

$\frac{A}{sin(a)}=\frac{B}{sin(b)}=\frac{C}{sin(c)}$

this example of triangle is perfect because we only need to replace the values of a,b,c for p,q,r

$\frac{P}{sin(p)}=\frac{Q}{sin(q)}=\frac{R}{sin(r)}$

since we know the value of R, r and q we can find Q with this sines law

R and Q represent angles and r and q represents sides

since we know r and q we know 2 sides of the triangle

then the answer is

Law of Sines, two sides and an opposite angle are known