Chapter 6.5, Problem 5E

To determine

To find height of the tree and to show the proportional ratios of sides:

Answer to Problem 5E

The height of the palm tree is 228 inches

And the proportional ratios are $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Explanation of Solution

Given information:

Consider the given triangles triangle be ABC which the pine tree casts shadow on the ground and DEF be the triangle which the man casts the shadow on the ground

And both the triangles are similar according to information.

Where AB $=x\text{ in}\text{ EF=26 in DE=74 in BC}=80\text{ in }$

And $\Delta ABC\sim \Delta DEF$

Let $x$ i.e. AB be the height of the pine tree in inches

Calculation :

Since both the triangles are similar,then the ratio of their corresponding sides will also be equal.

  $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{FD}$

  $=\frac{x}{74}=\frac{80}{26}$

  $=>x=\frac{80\times 74}{26}$

  $x=227.69in\text{ or }x=228in$