Question

The people of Lyria want to build a cable car to carry tourists to the top of Mount Sohcahtoa, which is 800 yards up. If the cable car must rise at an angle of 37, how long must the cable be to reach the top of the mountain?

Answer 1

Let's assume the length of the cable is x.

We need to find the hypotenuse x and the opposite side is AB = 800 yards is given. So, we can use sin ratio to find x. Because,

`sin\theta = (Opposite side)/(hypotenuse)`

So,
`Sin 37 = (800)/(x)`

`0.6018= (800)/(x)`

`0.6018*x= (800)/(x)*x`

0.6018 x = 800

`(0.6018x)/(0.6018) =(800)/(0.6018)`

So, x = 1329.345297

x = 1329 ( Rounded to nearest integer).

Hence, the length of cable must be 1329 yards.

Hope it's helps you!