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A portion of a hiking trail slopes upward at about a 6 degree angle. To the nearest tenth of a foot, what is the value of x, the hiker's change in vertical position, if he has traveled a horizontal distance of 120 feet?

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CastleRook
The vertical distance will be given by:
sin θ=opposite/hypotenuse
but
θ=6°
opposite=x
hypotenuse=120 ft
thus
sin 6=x/120
x=120 sin 6
x=12.54 ft
thus the hiker's change of position is 12.54 ft

The value of x, the hiker's change in vertical position, if he has traveled a horizontal distance of 120 feet would be 120.661 ft.

What is the cos formula in trigonometry?

The cos of an angle in a given right-angled triangle is the ratio of its adjacent side to the hypotenuse.

cos θ = adjacent / hypotenuse.

A portion of a hiking trail slopes upward at about a 6 degree angle.

cos θ = adjacent/hypotenuse

let the hypotenuse be h,

adjacent =120 ft, θ=6°

cos 6 = 120/h

h = 120/cos 6

h = 120.661 ft

Hence, The value of x, the hiker's change in vertical position, if he has traveled a horizontal distance of 120 feet would be 120.661 ft.

Learn more about cos function here;

https://brainly.com/question/9838343

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