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## Homework Statement

This last related rates HW problem is givin me trouble for some odd reason.

A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 25 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 1 minutes later?

## Homework Equations

Law of Cosines:

[tex]c^2=a^2+b^2-2abCos(\theta)[/tex]

[tex]a=11km[/tex]

[tex]b=4km[/tex]

[tex]\frac{da}{dt}=0[/tex]

[tex]\frac{db}{dt}=4km/min[/tex]

## The Attempt at a Solution

First using the law of cosines I found c at that particular moment.

[tex]c=\sqrt(137-88Cos(23\pi/36))[/tex]

Second I found the derivitive of the law of cosines

Working everything out I get:

[tex]\frac{dc}{dt}=\frac{16-44cos(23\pi/36)+44sin(23\pi/36)}{c}[/tex]

I plug in c and get the wrong answer, what did I do wrong?

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