Question

Two planes take off at a ny airport. The first plane climbs at an angle of 45 degrees with respect to the ground and reaches an altitude of 5600 feet. The second plane climbs at an angle of 60 degress with respect to the ground and reaches an altitude of 8200 feet. To the nearest foot, which plane covers a longer gorund distance?

Answer 1

well, since plane #1 is rising at 45°, its ground distance is equal to its altitude, or 5600.

The 2nd plane coves less ground than its altitude. It is 8200 cos 60° = 4100

Answer 2

I didn't learn trig. I'm in 7th grade. I did't learn it. Can you simplify it without trig please? I have a half hour before i leave for school

Answer 3

once you start tossing in angles, you'd better have some trig. Either that or know some basic facts about certain right triangles. I assume you have heard of the Pythagorean Theorem.

For this problem, draw a right triangle with the hypotenuse going from the starting point to the plane.

A 45° right triangle has both its legs the same length, so the ground covered is the same as the altitude.

A 60° triangle has its short leg 1/2 the hypotenuse. In fact, just saying that shows I made an error. I had said it was 1/2 the height, but that's not so. The long leg is √3 times the short leg. So, if the plane is 8200 feet high, it has gone 8200/√3 = 4734 feet on the ground.