Wpp13-14:concepts6-7 applications law of sines and cosine

WPP 13 & 14
 This WPP13-14 was made in collaboration with Louis Troung.  Please visit the other awesome posts on their blog by going here.
 Stephanie decides to go on a vacation with Louis after all her soccer tournaments were over.they end up going to a beachside house. there are two boats but they are both different colors one is blue and the other is red. Stephanies favorite color is blue just like louises so they are going to race for it. Stephanie is 10 feet away from Louis . Stephanie knows she ahs to turn
S30E and Louis need to turn N32E to get to the boat. which one of them is closer to the boat?

this is the visual we get from the word problem

 once we start using the hints we got for the angles we can now see that this triangle is an angle side angle and we can figure this out by using law of sines

as you can see in this picture we are going to figure out the missing angle that is left there bcause it will be the one pair we need to use law of sines we are going to subtract 180 from 32 and 30 because all triangle angles add up to 180 so that's how we are going to find out the missing angle after that you will just stat using the law of sines as you see in the picture leaving us with Louis being closer thus him getting to the boat faster.


On a nice day Stephanie and louis decide to go boating on our boats ! Stephanie and louis are 10 miles apart . Stephanie and louis know that louis has a bearing of 043 to Stephanie. The light house is 40 miles away from louis to the east I him .  Stephanie wants to go to the light house. How far is she from the light house ?