# Trigonometry problem

by amanara
Tags: trigonometry
 P: 3 Trigonometry problem Use the law of sines. The law of sines for a triangle is just the relation that the ratio of the sine of an angle by the length of the opposite side of the triangle is a constant for each triangle. With this law you can calculate the size of both sides of the triangle, or quicker you can just compare the two sides in question to see which one is bigger. Let PB be the distance from fire station P to building B. Let QB be the distance from Q to B, then $$\frac{PB}{sin(60\,degrees)}=\frac{QB}{sin(45\,degrees)}$$ $$\frac{2PB}{\sqrt{3}}=\frac{2QB}{\sqrt{2}}\Rightarrow PB=QB\frac{\sqrt{3}}{\sqrt{2}}>QB$$ which is what is to be expected from the angles. The second problem is done in a similar manner. Calculate the distance it has moved, and just divide by the time to get the average speed.