Question

A backcountry airport has a runway that is 150 feet long. Approximately 75 feet past the runway is a large

grove of trees that average in height around 100 feet tall. What angle of elevation must a pilot take in
order to avoid crashing into the trees? Round to the nearest hundredths.
Select an answer
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Answer 1

To find the angle of elevation, we need to determine the height of the plane relative to the trees, and then use the tangent function to find the angle. Let's call the height of the plane "h".

We can set up a right triangle with the height of the plane, the distance from the runway to the trees, and the height of the trees.

We have:

h / (150 + 75) = 100 / h

Solving for h, we find that:

h = 125

So the height of the plane relative to the trees is 125 feet.

Now we can use the tangent function to find the angle:

tan(angle) = 100 / 125

angle = tan^-1(100 / 125)

angle = approximately 53.13 degrees

Rounding to the nearest hundredths, the angle of elevation that the pilot must take to avoid crashing into the trees is 53.13 degrees.