In sunlight , a vertical stick has a height of 3 ft and casts a shadow 2 ft long. at the same time , that a nearby tree casts a shadow 20ft ling . how tall is the tree ? 1) 133 ft 2) 13.3 ft 3) 30 ft 4) 0.3 ft

30 ft

Explanation:

This problem may be solved by similarity of triangles.

Given that the angle of sun rays are the same for both the stick and the tree, the right triangles formed by their shadows, the object and the sun rays are similar. That means that their corresponding sides are proportional.

That leads to this proportion:

  height of the vertical stick        height of the tree
=
shadow of the vertical stick       shadow of the tree

      3 ft        x
=> =
      2 ft      20 ft

Now you can solve for x:

x = 20 ft * 3 ft / 2 ft = 30 ft.

30 ft.