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rate of change word problem?
An airplane is climbing at a 15 degree angle to the horizontal. How fast is it gaining altitude if its speed is 400 miles per hour?
So I know what the picture is supposed to look like:
http://pic90.picturetrail.com/VOL2363/11813548/209...
And I'm thinking that equation I'm supposed to use is
tan(15°) = Y/X
And I know how to take the derivative of that equation.
But the only other information I have is dX/dt = 400 mph
So how am I supposed to solve this without knowing any side lengths?
2 Answers
- normanLv 71 decade agoFavorite Answer
No derivatives, a = 400 tan15
that is the change in altitude in mph
- 1 decade ago
You don't need derivatives if you just use a right triangle
a
b . . . . . . . . . . c
The plane is traveling from c to a on a vector of length 400
the angle of c is 15 deg
you are looking for the length of the vector from b to a
Sine (c) = Opp/Hyp
0.2588 = (ab)/400
(ab) = 400*.2588 = 103.5