SOLUTION: Could you help me answer this question? A plane flies on a heading/bearing of 75 degrees at 460 mph. To the nearest hundredth how far is the plane from the airport at the end of 3.

Question 674325: Could you help me answer this question? A plane flies on a heading/bearing of 75 degrees at 460 mph. To the nearest hundredth how far is the plane from the airport at the end of 3.2 hours? How far east of the airport? How far north of the airport?
I calculated that it would travel 1472 miles in 3.2 hours.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
3.2 * 460 = 1472 which means the plan has traveled 1472 miles in 3.2 hours at 460 mph.
that part is correct.
the rest is trigonometry.
make a graph and then make a line that makes an angle of 75 degrees with the x-axis.
the line starts at the origin of the graph and extends upward to the right at the 75 degree angle from the x-axis.
you now can make a right triangle.
the hypotenuse is 1472 miles long.
the horizontal leg of this triangle represents the number of miles he travels in an easterly direction and the vertical leg of this triangle represents the number of miles he travels in a northerly direction.
the horizontal distance he travels we'll call x
the vertical distance he travels we'll call y
the hypotenuse we'll call z.
since this is a right triangle, then we get the following trigonometric relationships.
sin(75) = y/1472
cos(75) = x/1472
we use these equations to solve for x and y
y = 1472 * sin(75)
x = 1472 * cos(75)
use your calculator to solve for x and y
you should get:
y = 1421.842816
x = 380.9816344
x is the number of miles he traveled in an easterly direction.
y is the number of miles he traveled in a northerly direction.
z is the number of miles he traveled in a combined easterly and northerly direction at a 75 degree angle from the east.
the following diagram shows you what i mean.
$$$$$

in the diagram, the numbers are rounded.
z = 1472
x = 381
y = 1422
unfortunately, 1422 looks a lot like 1472 but if you look closely there is a difference. just bad handwriting on my part - sorry for that.

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