Question

shanley is 6 ft tall. he wants to stand in the shade of a tree that is 35ft tall. if the tree casts a 10 ft shadow, what is the farthest stanley can stand from the tree and be competely in its shadown?

Answer 1

Using similar triangles, Shanley can stand approximately 11.71 feet from the tree to be completely in its shadow.

Step-by-step explanation:

The question involves finding the maximum distance Shanley can stand from a tree and still be completely in its shadow. To solve this, we'll use similar triangles. The height of Shanley is to the height of the tree as the length of Shanley's shadow is to the length of the tree's shadow.

Let's call the farthest distance that Shanley can stand from the tree (and still be completely in the shade) d. The resulting proportion is:

Shanley's height / Tree's height = d / Tree's shadow

So,

6 ft / 35 ft = d / 10 ft

Multiplying both sides of the equation by 35 ft gives us:

d = (6 ft / 35 ft) × 10 ft

d ≈ 1.71 ft as the distance Shanley's shadow extends from the tree

To find the total distance from the tree, we add the length of Shanley's shadow (1.71 ft) to the length of the tree's shadow (10 ft), so Shanley can stand approximately 11.71 ft from the tree.