An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle elevation of the airplane's path?

Question

Abigail Allen · Accepted Answer

The angle of elevation is approximately #10.72^@#.

Putting everything in the same units is where we need to start. Let's convert #1# mile to feet. There are #5280# feet in a mile, so we can change the initial statement to "An airplane rises vertically 1000 feet over a horizontal distance of 5280 feet". The angle of elevation is measured by the horizontal, so the vertical rise will be opposite to the angle of elevation, #theta#, in the imaginary triangle we draw. The proper trigonometric ratio to use will be tangent, knowing that opposite measures #1000# feet and adjacent measures #5280# feet. #tantheta = 1000/5280# #theta = 10.72^@# I hope this is useful!

Eva Adamson · Answer

undefined To find the angle of elevation of the airplane's path, you can use trigonometry. The tangent of the angle of elevation is equal to the ratio of the height gained (1000 feet) to the horizontal distance traveled (1 mile = 5280 feet).

$ \tan(\text{angle of elevation}) = \frac{\text{height gained}}{\text{horizontal distance traveled}} = \frac{1000}{5280} $

Taking the arctangent of both sides gives:

$ \text{angle of elevation} = \arctan\left(\frac{1000}{5280}\right) $

Calculating this yields the angle of elevation.