Question

A zip line starts 28 feet in the air and

Answer 1

Given:

A zip line goes from 28 feet to 11 feet in the air. The angle of depression is 85°.

To find:

The length of the zip line where there is no rider.

Solution:

A right-angled triangle can be formed using the given data.

The difference in height between the start and end of the zipline is $28-11=17$. The angle of the triangle is 85°.

Assume the zip line is x feet long.

The adjacent side of the triangle measures 17 feet, the hypotenuse of the triangle measures x feet, and the angle of the triangle is 85°.

To determine x, we calculate the cos of the given angle.

$cos \theta = \frac{adjacentside}{hypotenuse} .$

$cos 85 = \frac{17}{x} , x = \frac{17}{cos85}, cos85= 0.0871.$

$x = \frac{17}{0.0871} = 195.1779.$

Rounding this off, we get the length of the zip line when there is no rider is 195.18 feet long.