Question

a tree casts a shadow 8 feet long. A 6-foot Man cast a shadow 4 feet 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

Answer:

12 feet

Step-by-step explanation:

Draw a diagram (see picture below). The tree and its shadow is one triangle, the man and its shadow is another triangle. We assume both are right triangles because people and trees stand vertical.

Create a proportion to solve. Put the missing value in a numerator.

Tree height / Tree shadow = Man height / Man shadow

$\frac{x}{8} =\frac{6}{4}$

Solve using cross multiplication. Multiply x by 4. Multiply 6 by 8.

4x = 48    Divide both sides by 4 to isolate x.

x = 12       Height of tree

The tree is 12 feet tall.