Question

The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 68 inches tall casts a shadow 81 inches long, how tall is a tree which cast a shadow 33 feet in length

Answer 1

To find the height of the tree, we can set up a proportion using the concept of direct variation. Given that the shadow of the tree is 33 feet in length, which is equivalent to 396 inches, the height of the tree is approximately 472 inches.

Step-by-step explanation:

To solve this problem, we can set up a proportion using the concept of direct variation.

We have the height of the person, 68 inches, and the length of their shadow, 81 inches. Let's call the height of the tree x and the length of its shadow y.

We can set up the proportion: 68/81 = x/y

To find the height of the tree, we can cross-multiply and solve for x:

68y = 81x

x = (68/81)y

Given that the shadow of the tree is 33 feet in length, which is equivalent to 396 inches, we can substitute this value into the equation:

(68/81)y = 396

Solving for y, we get:

y = (81/68) * 396

y ≈ 472 inches

Therefore, the height of the tree is approximately 472 inches.