Question 615991: Can someone PLEASE help me with this word problem? THANK YOU!
A man is flying in a hot-air balloon in a straight line at a constant rate of 5
feet per second, while maintaining it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35(degrees). A minute and a half later, after flying directly over his friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36(degrees). At that time, what is the distance between him and his friend? (Round to the
nearest foot.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i solved this the hard way.
then i remembered the law of sines.
that made it easy (i think).
law of sines says that a/sin(A) = b/sin(B) = c/sin(C)
label the starting point of the balloon as point A.
label the ending point of the balloon as point B.
label the position of the car as point C.
the side of the triangle representing the distance the balloon travels is the side AB which we call side c because it is opposite angle C.
the side of the triangle representing the distance from where the balloon takes the 36 degree angle (point B) to the car (point C) is equal to the line segment BC which we call side a because it is opposite angle A.
we know that the side c is equal to 450 feet because the balloon travels 5 feet per second and it takes the balloon 90 seconds to go from point A to point B.
we know that angle A is equal to 35 degrees and angle B is equal to 36 degrees.
that makes angle C equal to 109 degrees because the sum of the angles of a triangle is equal to 180 degrees.
the formula we will use will be:
a / sin(A) = c / sin(C)
angle A is 35 degrees
angle C is 109 degrees
c is equal to 450 feet
a is what we want to find.
the formula becomes:
a / sin(35) = 450 / sin(109)
multiply both sides of this equation by sin(35) to get:
a = 450 * sin(35) / sin(109)
use your calculator to solve for a to get:
a = 272.9818356
round to the nearest foot to get:
a = 273 feet
i solved it a harder way using trigonometry and got the same answer so i'm reasonably confident that it's right.
you should be able to draw yourself a diagram, but if you have problems with that, let me know and i'll send you a picture.
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