How fast is the plane traveling at that time?

A plane flies horizontally at an altitude of 1 km and passes directly over a tracking telescope on the ground. When the angle of elevation is 蟺/3, this angle is decreasing at a rate of 蟺/3 rad/min. How fast is the plane traveling at that time? (Round your answer to two decimal places.)How fast is the plane traveling at that time?horizontal distance = D (in kilometers)

Angle of elevation = A



tan (A) = 1 / D

D = 1 / tan(A) = cot(A)



dD/dt = dD/dA * dA/dt



. . . dD/dA = - csc^2(A)



dD/dt = - csc^2(A) * dA/dt



. . . given A = 蟺/3 and dA/dt = - 蟺/3



dD/dt = - csc^2(蟺/3) * (- 蟺/3)



dD/dt = 4 蟺 / 9 km per min



83.7758 km per hour ... seems to slow for real life, but there it is.