Question

You and a friend want to know how much rope you need to climb a large rock. your friend is 5.5 feet tall and casts a shadow that is 18 feet long. if the rock casts a shadow that is 209.5 feet long, calculate the height of the rock from the ground. round your answer to the nearest foot. (hint: make a drawing)

Answer 1

To the nearest feet, the rock is 64 feet tall.

Explanation:

Height of the friend = 5.5 feet

Height of friend's shadow = 18 feet

Height of the rock's shadow = 209.5 feet

Let the height of the rock be = x

We can represent this situation is ratio form.

`(5.5)/(18)= (x)/(209.5)`

=>
`18x=209.5*5.5`

=>
`18x=1152.25`

=>
`x=64.01`

So, to the nearest feet, the rock is 64 feet tall.

Answer 2

The concept useful in finding the answer to this item is ratio and proportion, the ratio of the height of your friend with the shadow casted should be proportional to the height of the rock with the length of the shadow it cast. That is,
5.5 ft / 18 ft = x ft/ 209.5 ft
The value of x from the equation above is 64 ft.