Question

The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 26. if the vertical distance from the bottom to the top of the mountain is 725 feet and the gondola moves at a speed of 180 feet per minute, how long does the ride last? round to the nearest minute.

a. 4 minutes
b. 5 minutes
c. 9 minutes
d. 8 minutes

Answer 1

To find the duration of the gondola ride, calculate the hypotenuse using the sine of the angle of elevation and the known vertical distance, then divide by the gondola's speed and round to the nearest minute.

Step-by-step explanation:

To calculate the length of the gondola ride, we need to find the hypotenuse of the right triangle formed by the angle of elevation, the vertical distance (725 feet), and the hypotenuse (the path of the gondola). We can use the sine of the angle of elevation to do this:

sin(26°) = vertical distance / hypotenuse

sin(26°) = 725 / hypotenuse

hypotenuse = 725 / sin(26°)

Find the length of the hypotenuse, then divide that length by the speed of the gondola (180 feet per minute) to find the time in minutes it takes for the gondola to travel to the top of the mountain. Round this time to the nearest whole number to find the duration of the ride.