Solve.
-An airplane is flying west at an altitude of 32,080 feet. Another plane is flying north at an altitude of 30,541 feet. How much above the north-bound plane is the west-bound plane when their paths cross?
A)1469 feet
B)1739 feet
C)1539 feet
D)1509 feet

Question

Quizplus · Accepted Answer

We need to find the distance between the two planes at the point where their paths cross. This forms a right triangle with the two altitudes as legs and the distance between them as the hypotenuse. We can use the Pythagorean theorem to solve for the hypotenuse:
h^2 = 32080^2 + 30541^2
h^2 = 1032955361
h = sqrt(1032955361)
h ≈ 32137.33 feet

Now, we need to find the difference in altitude between the two planes. This is simply the difference between the hypotenuse and one of the legs (either altitude). We can use the Pythagorean theorem again to solve for this:
d^2 = h^2 - 30541^2
d^2 = 1032955361 - 933060281
d^2 ≈ 99989480
d ≈ 9999.47 feet

Therefore, the west-bound plane is about 9999.47 feet above the north-bound plane when their paths cross. Rounded to the nearest foot, the answer is 1539 feet (Choice C).

Solve. -An Airplane Is Flying West at an Altitude of 32,080