Question

A tree casts a shadow 60ft long. A 6ft man casts a shadow 8ft long. The triangle formed by the tree and its shadow is similar to the triangle formed by the man and his shadow. How tall is the tree?

Answer 1

The tree is 45ft tall.

Step-by-step explanation:

The problem involves solving for the height of a tree given the shadow length of the tree and a 6ft man. Since the triangles formed by the tree and its shadow, and the man and his shadow are similar, we can set up a proportion to find the height of the tree.

Let's denote the height of the tree as 'x'. The proportion will be:

(Height of the tree) / (Length of the tree's shadow) = (Height of the man) / (Length of the man's shadow)

Substituting the given values, we get:

x / 60 = 6 / 8

Cross-multiplying and solving for 'x', we find:

x = (6 / 8) * 60

x = 45ft

Therefore, the tree is 45ft tall.