a zipline starts 25 feet. off the ground and has an angle of elevation of 27 degrees. what is the horizontal distance the zipline will cover,x?
We have a right triangle formed by the zipline, the ground, and a vertical line. The angle of elevation is the angle between the ground and the zipline.
The opposite side of the right triangle is the height of the zipline, which is 25 feet.
The adjacent side of the right triangle is the horizontal distance covered by the zipline, which is x.
The hypotenuse of the right triangle is the length of the zipline.
Using the trigonometric function tangent, we can set up the following equation:
tan(27 degrees) = opposite/adjacent
tan(27 degrees) = 25/x
To solve for x, we rearrange the equation:
x = 25/tan(27 degrees)
Using a calculator, we find that tan(27 degrees) is approximately 0.5095. Plugging this value into the equation:
x = 25/0.5095
x ≈ 49.04
Therefore, the horizontal distance the zipline will cover is approximately 49.04 feet.