Question

Approximately how much more quickly (in mph) does a pilot traveling 400 mph and rising at an angle of 30o gain altitude versus a pilot traveling 300 mph and rising at an angle of 40o?

Answer 1

We can find the height of the altitude by the ratio of sin. See my attachment.
sin of angle = side in front of the angle / hypotenuse
sin x = height/distance

If the two pilot is rising in an hour, then the first distance is 400 miles, the second distance is 300 miles.

Find the height of first pilot
height/distance = sin x 
height/400 = sin 30°
height = sin 30° × 400
height = 1/2 × 400
height = 200

Find the height of second pilot
height/distance = sin x 
height/300 = sin 40°
height = sin 40° × 300
height = 0.642 × 300
height = 192

So the first pilot traveling 400 mph with 30° is more quickly to reach high altitude than the second pilot traveling 300 mph with 40°