An airplane is approaching Los Angeles International Airport at an altitude of 10,560 feet. If the horizontal distance from the plane to the runway is 2.1 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (see the figure below). (5,280 feet equals 1 mile.) a = 2.1 miles, b = 10,560 feet
A)2.6 miles
B)2.2 miles
C)2.9 miles
D)2.3 miles
E)2.8 miles

Question

An airplane is approaching Los Angeles International Airport at an altitude of 10,560 feet. If the horizontal distance from the plane to the runway is 2.1 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (see the figure below). (5,280 feet equals 1 mile.)  a = 2.1 miles, b = 10,560 feet
A)2.6 miles 
B)2.2 miles 
C)2.9 miles 
D)2.3 miles 
E)2.8 miles

Quizplus · Accepted Answer

We need to find the diagonal distance which is represented by the hypotenuse of the right triangle formed by the altitude and the horizontal distance. Using the Pythagorean Theorem: 
hypotenuse^2 = altitude^2 + horizontal distance^2 
= (10,560)^2 + (2.1 miles x 5,280 feet/mile)^2 
= 111,513,600 + 232,848 
= 111,746,448 
Taking the square root: 
hypotenuse = 3342.17 feet 
Converting to miles: 
3342.17 feet / 5,280 feet/mile = 0.63 miles 
Therefore, the diagonal distance from the plane to the runway is approximately 2.1 + 0.63 = 2.73 miles or 2.9 miles (rounded to one decimal place). The best choice is C).

An Airplane Is Approaching Los Angeles International Airport at an Altitude