The angle of elevation from the bottom of a scenic gondola ride to the top of the mountain is 22. if the vertical distance from the bottom to the top of the mountain is 689 feet. what is the length of the gondola ride? round to the nearest foot.
a: 1839ft
b: 743
c: 258
d: 634

  A:  1839 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles of a right triangle. Here you have an angle and its opposite side, and you want to find the length of the hypotenuse. The appropriate relation is ...

  Sin = Opposite/Hypotenuse

  sin(22°) = (689 ft)/(ride length)

Solving for ride length, we get ...

  ride length = (689 ft)/sin(22°) ≈ 1839.26 ft

The length of the gondola ride is about 1839 feet.

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²