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

The drawing shows the rock height to be 64 ft.

The shadow lengths are proportional to the object heights, so we have
   (rock height)/(209.5 ft) = (5.5 ft)/(18 ft)
   (rock height) = (209.5 ft)*(5.5/18) ≈ 64.01 ft

The height of the rock from the ground is about 64 ft.