Question

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?

Answer 1

$\sin( \alpha ) = \: \frac{opp}{hyp}$
$\sin(22) = \frac{689}{hyp}$
$hyp \: = \frac{689}{ \sin(22) }$
$speed = \frac{distance}{time}$
$time = \frac{ \frac{689}{ \sin(22) } }{130} \: \: \:minutes$

Answer 2

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Using SOH CAH TOA in right triangle,

$sin 22=\frac{opposite}{hypotenuse}$

$sin 22=\frac{689}{x}$

$x=\frac{689}{sin 22}$

Plugging the value of sin 22

$x=\frac{689}{0.3746}$

$x=1839.29$ feet

So the distance is 1839.29 feet.

$time=\frac{distance}{speed}=\frac{1839.29}{130}$

time=14.15 minutes   :    Answer

Hope it will help :)