an airplane is flying at an altitude of 3200 feet. an air- traffic controller in the tower keeps constant track of the planes distance from the tower in X feet. express the horizontal distance from the tower to a point directly below the airplane,d, in terms of X.
the distance x is the hypotenuse of a right triangle with legs d and 3200.
d^2 = x^2 - 3200^2
To find the horizontal distance from the tower to a point directly below the airplane, we need to use the altitude and the distance from the tower. Let's assume the distance is X feet.
We can visualize the situation as a right triangle. The vertical leg represents the altitude of the airplane (3200 feet), the horizontal leg represents the horizontal distance from the tower to the point directly below the airplane (d feet), and the hypotenuse represents the distance from the tower to the airplane (X feet).
Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can set up the equation:
d^2 + 3200^2 = X^2
To express the horizontal distance from the tower to the point directly below the airplane (d) in terms of X, we need to isolate the variable d. Rearranging the equation, we get:
d^2 = X^2 - 3200^2
Taking the square root of both sides, we have:
d = √(X^2 - 3200^2)
Therefore, the expression for the horizontal distance from the tower to a point directly below the airplane (d) in terms of X is √(X^2 - 3200^2).