WPP #13 & 14: Unit P Concept 6 & 7 Law of Sines and Cosines.

This WPP13-14 was made in collaboration with Judith Quintanilla.  Please visit the other awesome posts on their blog by going Here .
Problems.

Law of cosines.

Billy Bob Joe Ray Eugene III decided to go quad racing with Camila. When they leave the lot where they rent the quads, Billy rode 70mph N52E. Camila rode at 80mph. and at an angle of 110 degrees bearing. suppose they rode for 3 hrs. and went in a straight line. How far would they be from each other?

Law of Sines

Camila and Billy Bob Joe Ray Eugene III want to race. They both see a red flag that is 240 ft from Camila and The angle formed at Camila is 54.14 degrees. The angle with Billy's is 58 degrees. How far is Billy from the flag? Is this fair?

Solutions

Cosines

In order to find how far they are we use the law of cosines. we plug x^2=240^2+210^2-2(240)(210)Cos58. and we get x=219.74 miles.

Sines

Sine we Know <A, Side a, and <B, we need to find side b. we get sin54.14/a=sin58/240. we manipulate it to get a by itself so it'll be a=240Sin54.14/Sin58 and we get a=229.36 ft. Billy side was shorter and he won the race!! WOOHOO!!