An airplane is flying east at an altitude of 28,000 ft. When Lizzie first sees it, the plane is to the east of?

With the first observation, the height of 28,000 feet is Opposite the angle of 71.5°.

You want to know the horizontal distance (D), which is the Adjacent side.

Tthe Hypotenuse is the Lizzie-to-plane distance, which we don't need.

Opposite over Adjacent is tan, so

tan 71.5 = 28,000 / D

D tan 71.5 = 28,000

D = 28000 / tan 71.5

D = 28000 / 2.988684962...

D = 9,368.668946... feet

So the plane is around 9,368 horizontal feet away from Lizzie.

For the second observation, the height hasn't changed but the angle has, so the new distance (N) has changed too. So the formula is now

N = 28000 / tan 40

N = 28000 / 0.839...

N = 33,369.1... feet

That means that in 30 seconds, the plane travelled 33,369-9368.5 = 24,000.1... feet

That means that in a minute, the plane would travel 24,000x2 = 48,000 feet

That means that in 60 minutes, or an hour, the plance would travel 60x48,000 = 2,880,000 feet

There are 5,280 feet in a mile. That means that in an hour, the plane would travel 2,880,000/5,280 = 545.4545454545... miles

If you do all the calculations using full decimal places (not rounded like I have above!), you actually get 545.46435560408704993179017943117

Therefore, the plane is going at 545.464 miles per hour.

Speed of Airplane is given by

28000 [cot 40 -- cot 71.5]*3600 / 30*5280 mph ANSWER

I DON'T HAVE CALCULATOR.