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?

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

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

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.

To determine which plane covers a longer ground distance, we need to calculate the horizontal distances traveled by each plane.

Let's start with the first plane. The angle of ascent is given as 45 degrees, and the altitude reached is 5600 feet. We can use trigonometry to calculate the horizontal distance.

In a right-angled triangle, the horizontal distance (adjacent side) can be calculated using the formula:

horizontal distance = altitude / tangent(angle)

For the first plane:

horizontal distance = 5600 feet / tangent(45 degrees)

Using a scientific calculator, the tangent of 45 degrees is 1.

So, the horizontal distance traveled by the first plane is 5600 feet.

Now, let's calculate the horizontal distance for the second plane. The angle of ascent is given as 60 degrees, and the altitude reached is 8200 feet.

For the second plane:

horizontal distance = 8200 feet / tangent(60 degrees)

Using a scientific calculator, the tangent of 60 degrees is approximately 1.732.

So, the horizontal distance traveled by the second plane is approximately 8200 feet / 1.732 = 4738.56 feet.

Rounding both values to the nearest foot, we find that the first plane covers a longer ground distance, approximately 5600 feet, compared to the second plane's 4739 feet.

Therefore, to the nearest foot, the first plane covers a longer ground distance.