Question

On a sunny day, a 6-foot tall man positions himself so that his shadow lines up with the end of the shadow of a palm tree. The man's shadow is 8 feet long, and he is standing 16 feet from the base of the palm tree, as shown below.

Answer 1

The question involves applying geometric concepts, specifically similar triangles, in practical scenarios to estimate the height of a tree using a man's known height and shadow length.

Step-by-step explanation:

The question discussed involves the use of similar triangles to deduce the height of an object (a palm tree) using the known heights and shadows of another object (a man).

Since this question revolves around the shadow lengths and heights of objects, which are related to the angles and proportions that are consistent in similar geometric figures, it falls squarely within the purview of Geometry, a branch of mathematics.

By employing the principles that dictate the behavior of shadows during different times of the day, notably when the Sun is at its peak, we can make accurate estimations of heights and distances.

In this context, the height of the man and the length of his shadow are used in proportion with the unknown height of the tree and its shadow to find the answer. This method works because the sun's rays are considered to be parallel, leading to proportional relationships between the lengths of shadows and their corresponding objects.