A pilot needs to know if a plane with clear the tower. The plane will travel 1300 yards before lifting off the ground to travel another 705 yards after which point the plane will be directly over the tower. If the plane had continued on the runway, it is another 700 yards to the control tower, which is 250 feet high.

The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

Step-by-step explanation:

The given parameters are;

The length the plane will travel before lifting = 1300 yards

The distance further the plane will travel after lifting off the ground = 705 yards

The horizontal distance from the point of lifting off the ground to control tower = 700 yards

The distance of the path of the plane after lifting off the ground, the horizontal distance from the point of lifting off the ground to control tower and the height of the control tower form a right triangle with sides given as follows;

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle

Let h, represent the height of the control tower, let x represent the horizontal distance from the point of lifting off the ground to control tower and let R represent the distance of the path of the plane after lifting off the ground, we have;

h = √(R² - x²)

We have;

R = 705 yards

x = 700 yards

∴ h = √(R² - x²) = h = √(705² - 700²) = 5·√281

The height of the control tower, h = 5·√281 yards

1 yard = 3 feet

∴ 5·√281 yards = 3 × 5·√281 feet ≈ 251.446 feet

Therefore, given that the height of the control tower = 250 feet, the plane at the height of approximately 251.446 feet clears the tower.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.