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? Round to the nearest minute.
+33661 Use sin(22°) = 689/h where h is the length of the gondola wire, to get h = 689/sin(22°) feet.
Then divide h by 130 feet per minute to get the ride time in minutes.
ride time = 689/(sin(22°)*130) minutes
$${\frac{{\mathtt{689}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{22}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{130}}\right)}} = {\mathtt{14.148\: \!175\: \!961\: \!532\: \!953\: \!6}}$$
ride time = 14 minutes to the nearest minute.
+33661 Use sin(22°) = 689/h where h is the length of the gondola wire, to get h = 689/sin(22°) feet.
Then divide h by 130 feet per minute to get the ride time in minutes.
ride time = 689/(sin(22°)*130) minutes
$${\frac{{\mathtt{689}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{22}}^\circ\right)}{\mathtt{\,\times\,}}{\mathtt{130}}\right)}} = {\mathtt{14.148\: \!175\: \!961\: \!532\: \!953\: \!6}}$$
ride time = 14 minutes to the nearest minute.
