Implicit differentiation applications (exam tomorrow!)
Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 30 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 3 minutes later?
A: I let the trangle sides be A, B, and C; A is the initial distance between
radar and the plane (4km); B is the distance between initial position of
the plane to 3 mins later (24km x 3min = 72); C is the final distance between radar to plane.
so I have C^2 = 4^2 + 72^2 - (2)(4)(72)cos(120 degrees)
Solved for C = 5488km, but the answer is wrong...
What was wrong? Thank you.