Question

Justin is 74 inches tall and casts a shadow that is 102 inches long. At the same time, a tree casts a shadow that is 39 feet long. How tall is the tree to the nearest foot?

Answer 1

28.2941 feet

Explanation:

First we need to imagine a triangle with Justin and his shadow, and the tree and its shadow (as shown in the figure attached)., and then calculate the relation between Justin's height and his shadow's height

The relation between the opposite cathetus (height of Justin) and the adjacent cathetus (height of the shadow) is the tangent of the angle, so:

tan(angle) = 74/102 = 0.7255

The tree and its shadow will have this same angle and therefore this same relation, so:

0.7255 = tree / 39

tree = 0.7255 * 39 = 28.2941 feet