Question 288384: I don't understand how to solve these two question. Can someone please explain in detail?
1. A ranger in fire tower A spots a fire at a direction of 40 degrees. A ranger in fire tower B, which is 28 miles away directly east of tower A, spots the same fire at a direction of 330 degrees. How far from tower A is the fire?
2. A boat leaves the dock and sails in a direction of 70 degrees. Once reaching its destination on the opposite shore, it sails in a direction of 272 degrees and docks 150 km north of its original starting position. What is the total distance the boat has traveled?
I appreciate your help.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1. A ranger in fire tower A spots a fire at a direction of 40 degrees. A ranger in fire tower B, which is 28 miles away directly east of tower A, spots the same fire at a direction of 330 degrees. How far from tower A is the fire?
---------------------------
Directions are given using North as 0/360º
Points A, B and the fire (point F) form a triangle. Side AB is 28 miles
Angle A is 90 - 40 = 50º
Angle B is 60º (330-270)
Angle F is 70º (180 - 50 - 60)
Use the law of sines to find AF
AF/sin(60) = 28/sin(70)
AF =~ 25.805 miles
------------------
2. A boat leaves the dock and sails in a direction of 70 degrees. Once reaching its destination on the opposite shore, it sails in a direction of 272 degrees and docks 150 km north of its original starting position. What is the total distance the boat has traveled?
------------------------
S = starting point
D = destination
N = point 150 km north of S
-------------------
Side SN = 150 km
Angle S = 70º
Angle D = 22º
Angle N = 88º
Use the Sine Law as above.
------------------
Getting the angles from the given directions isn't familiar to most people.
Email me and I'll send sketches showing how it's done.
|
|
|
