Chapter 8.4, Problem 9PSA

To determine

To find the height of the tree.

Answer to Problem 9PSA

The tree was 25 m tall.

Explanation of Solution

Given information:

A tree was casting shadow of 30 m. A flagpole was casting 24 m shadow. A flagpole is of height 20 m.

Formula used:

The below properties are used:

Corresponding sides of similar triangles are proportional.

Means extremes product theorem:

If a product of a pair of not zero numbers is equal to the product of another pair of not zero numbers, then either pair of numbers be made the extremes, and the other pair the means, of proportion.

Calculation:

  

Corresponding sides of similar triangles are proportional.

  $\text{20/24 =x /30}$

Applying means extremes product theorem, we get

  $\begin{array}{l}\text{20*30 = 24*x}\\ \text{600 =24x}\\ \text{x= 25 }\end{array}$

The tree was 25 meter tall.