Solution:

Drew the right triangle as follows: Vertical segment labeled 5000 m = 5 km, assigned variable hj. At the top, a stick figure of a jet plane. Horizontal segment labeled 5 km, assigned variable b. Hypotenuse labeled 10 km, assigned variable c. The 5 and the 10 we get from the 30-60-90 relationship. Angle of elevation is angle , labeled = 30 deg (using degree symbol).

We also know that = 500 km/h and = 0. So,

tan = h/b and

sec

^{2}d/dt = (b dh/dt - h db/dt)/h

^{2}

Plugging in,

sec

^{2}d /dt = (0 - 5*500)/25 = -100. But sec = 10/5sqrt3, then sec

^{2}= 4/3 and

4/3 d /dt = -100. Multiplying both sides by 3/4 gives d /dt = -75; i.e. -75 radians/h.

Using a calculator, I get -75 /h * 1 h / 60 min * 1 min / 60 s = approx -0.0208333333 / s which converts to -1.19+°, or (-1 deg 11 min 37.2 sec) /s , answer