ski-lift cables aren't string at an angle 30 ° to the top of a 5000 ft mountain. How long are the cables?

Answer: the length of the cable is 10000 feet.

Step-by-step explanation:

A right angle triangle is formed. The length of the cable represents the hypotenuse of the right angle triangle. The height of the mountain represents the opposite side of the right angle triangle. To determine the length of the cable, L, we would apply the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 30 = 5000/L

L = 5000/Sin 30 = 5000/0.5

L = 10000 ft

The cables are 5,060.567 ft

You use tan to find this because 5000 is the opposite and your are trying to find the adjacent to the angle so then you can do Pythagorean theorem to find the length of the cables

Tan (30) = 5000/x

Multiply x on both sides

X•tan (30) = 5000

Divide by tan (30)

X = 5000 / tan (30)

X = - 780.5997608

Then you plug it in because x is the bottom length of the right triangle and now your finding the hypotenuse, the length of the cables

-780.5997608^2 + 5000^2 = x^2

609,335.9866 + 25,000,000 = x^2

25,609,335.99 = x^2

Then you square root the number

And x = 5,060.566766 ft

And your just round to the nearest hundredth or tenth like it did up too