An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle of elevation of the airplane's path? (hint: 1 mile = 5280 feet)

First of Jenn, he's asking for the ANGLE of a triangle, not the hypotenuse.

And the method you want to use is Tan x = 1000/5280

probably, if it doesnt work, than you're on your own

use a^2 + b^2 = c^2

a=1000
b=5280

First, let's convert the horizontal distance of 1 mile into feet. 1 mile is equal to 5280 feet.

Now, the airplane rises 1000 feet vertically and moves 5280 feet horizontally.

To find the angle of elevation, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side (height) to the adjacent side (horizontal distance).

So, the tangent of the angle of elevation can be calculated as:

tangent(angle) = height / horizontal distance

tangent(angle) = 1000 feet / 5280 feet

Simplifying this fraction, we get:

tangent(angle) = 0.1894

To find the angle itself, we need to take the inverse tangent (or arctan) of 0.1894.

Using a calculator or an arctan table, we find that the angle is approximately 10.83 degrees.

Therefore, the angle of elevation of the plane's path is approximately 10.83 degrees.

To find the angle of elevation, we can use trigonometry. In this case, we have a right triangle, where the height of the triangle is 1000 feet and the base of the triangle is 1 mile, which is equal to 5280 feet.

The angle of elevation is defined as the angle between the line of sight from the observer (horizontal line) to the object (airplane's path) and the horizontal ground.

Let's consider the right triangle formed by the vertical distance, horizontal distance, and the line of sight from the observer. The opposite side of the angle of elevation will be the height of the triangle (1000 feet), and the adjacent side will be the horizontal distance (5280 feet).

Using the tangent function (tan), we can find the angle of elevation:

tan(angle) = opposite/adjacent
tan(angle) = 1000/5280

To find the angle, we take the inverse tangent (also called arctan or atan) of both sides:

angle = atan(tan(angle)) = atan(1000/5280)

Using a calculator to evaluate atan(1000/5280), we find that the angle of elevation is approximately 10.68 degrees.