SOLUTION: A car leaves a gas station and travels at 30 miles per hour (mpg) due west. After 20 minutes, the car changes direction to N 30 W at 20 mph and travels in that direction for 15 min

Question 1136407: A car leaves a gas station and travels at 30 miles per hour (mpg) due west. After 20 minutes, the car changes direction to N 30 W at 20 mph and travels in that direction for 15 minutes. Find the car's distance traveled and the bearing from the gas station.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Drawing this helps.
Direction is left along the y-axis (bearing 270 degrees) and then at a 60 degree angle into quadrant II. That bearing is 330 degrees,
The first distance is 10 miles (20 min at 30 mph)
The second distance is 5 miles
Along the y-axis, that distance is another 2.5 miles left and upward (5/2) sqrt (3) miles
The car has traveled at total of 15 miles. ANSWER
The horizontal leg is 12.5 miles, and the vertical leg is 4.33 miles.
The car's straight line distance from the station is 13.23 miles
The cosine of the angle from the horizontal (bearing 270) is 12.5/13.23=0.9449
That angle is 19.10 degrees, so the car is bearing 289.1 degrees or W 19.1 N or N 70.9 W ANSWER

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