A portion of a hiking trail slopes downward at about an 84° angle. To the nearest tenth of a foot, what is the value of x, the distance the hiker traveled along the path, if he has traveled a horizontal

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Stas Korzovsky asked Nov 17, 2023

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A portion of a hiking trail slopes downward at about an 84° angle. To the nearest tenth of a foot, what is the value of x, the distance the hiker traveled along the path, if he has traveled a horizontal distance of 120 feet? B 849 А 120 ft С O A. 12.5 ft B. 130.2 ft C. 143.3 ft O D. 120.7 ft

A portion of a hiking trail slopes downward at about an 84° angle. To the nearest-example-1

Mathematics
college

Stas Korzovsky asked Nov 17, 2023

by Stas Korzovsky

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1 Answer

27 votes

The given figure form a triange right angled at A.

AC=120 ft.

BC=x.

BC is the hypotenuse.

Now, applying trigonometric property in the triangle,

$\begin{gathered} \sin Substitute the values.[tex]\begin{gathered} \sin 84\degree=(120)/(x) \\ x=(120)/(\sin 84\degree) \\ x=120.7\text{ ft} \end{gathered}$

Therefore, the value of x is 120.7 ft.

Abhijeet Kushe answered Nov 23, 2023