A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 7 km and climbs at an angle of 45 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 2 minutes later?

Question

I know you use law of cosines.

Write a formula for distance at any given time.

The derivate of this distance is the rate at which distance increases.

Draw the triangle. One leg vertical, 7km. The other two legs are from the top of the vertical @45 det to the plane (distance is 28km), the last leg is from the observer to the plane.

Figure by the law of cosines the distance from the observer to the plane.

Now, take derivative of the written law of cosines. You will have all you need. I will be happy to critique your work.