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The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22°. If the vertical distance from the bottom to the top of the mountain is 689 feet and the gondola moves at a speed of 130 feet per minute, how long does the ride last?

Respuesta :

Fiction248

[tex] \sin( \alpha ) = \: \frac{opp}{hyp} [/tex]
[tex] \sin(22) = \frac{689}{hyp} [/tex]
[tex]hyp \: = \frac{689}{ \sin(22) } [/tex]
[tex]speed = \frac{distance}{time} [/tex]
[tex]time = \frac{ \frac{689}{ \sin(22) } }{130} \: \: \:minutes[/tex]
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Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Using SOH CAH TOA in right triangle,

[tex]sin 22=\frac{opposite}{hypotenuse}[/tex]

[tex]sin 22=\frac{689}{x}[/tex]

[tex]x=\frac{689}{sin 22}[/tex]

Plugging the value of sin 22

[tex]x=\frac{689}{0.3746}[/tex]

[tex]x=1839.29[/tex] feet

So the distance is 1839.29 feet.

[tex]time=\frac{distance}{speed}=\frac{1839.29}{130}[/tex]

time=14.15 minutes   :    Answer

Hope it will help :)

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