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 [tex]28-11=17[/tex]. 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.
[tex]cos \theta = \frac{adjacentside}{hypotenuse} .[/tex]
[tex]cos 85 = \frac{17}{x} , x = \frac{17}{cos85}, cos85= 0.0871.[/tex]
[tex]x = \frac{17}{0.0871} = 195.1779.[/tex]
Rounding this off, we get the length of the zip line when there is no rider is 195.18 feet long.
The length of the zip line when there is no rider is 195.18 feet long.
Here the difference is
= 28 - 11
=17
And, The angle of the triangle is 85°.
Here we Assume the zip line should be x feet long.
Now
The length should be
[tex]cos\ 85 = 17\div x\\\\x = 17\div 0.0871[/tex]
= 195.18
Hence, The length of the zip line when there is no rider is 195.18 feet long.
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