Chapter 6.9, Problem 10PPS

To determine

The height of different poles if the tallest pole is 50 feet high and distance between two poles is 100 feet given.

Answer to Problem 10PPS

The heights of different poles, starting from first pole are 37.5 feet, 25 feet and 12.5 feet.

Explanation of Solution

Given information: 

The height of tallest pole is 50 feet and its distance from a given point on ground is 400 feet and in between there are three more poles so that distance between two poles is 100 feet.

Concept used: As both triangles, the largest one and any smaller one, are similar given, so the ratios of corresponding sides are proportional, so

  $\frac{\text{Height of the small pole}}{\text{Height of the tallest pole}}=\frac{\text{Distance of smaller pole from given point}}{\text{Distance of tallest pole from given point}}$

Calculation: As the distance of first pole from tallest pole, is 300 feet remaining, so using above proportion,

  $\frac{\text{Height of first pole from tallest pole}}{50}=\frac{300}{400}$

Or, height of the first pole from tallest pole $=\frac{300\times 50}{400}=\frac{150}{4}=37.5$ feet.

Again, the distance of second pole from tallest pole, is 200 feet remaining, so using above proportion,

Or,

  $\begin{array}{l}\text{Height}\text{of}\text{second}\text{}\text{pole}=\frac{200\times 50}{400}\\ =25\text{}\text{feet}\end{array}$

And similarly, the distance of third pole from tallest pole, is 100 feet remaining, so using above proportion,

Or, height of the third pole from tallest pole $=\frac{100\times 50}{400}=12.5$ feet

By above calculation, it is concluded that the heights of in between poles be 37.5 feet, 25 feet and 12.5 feet.