Chapter 6.9, Problem 12PPS

a)

To determine

To write: Two different proportions that could be used to find the height of the light house.

Answer to Problem 12PPS

Two different proportions are :

  $\frac{\text{Height of lighthouse}}{\text{Height of building}}=\frac{\text{Distance of lighthouse from given point}}{\text{Distance of building from given point}}$

And

  $\frac{\text{Height of lighthouse}}{\text{Height of building}}=\frac{\text{Distance of lighthouse top point from given point}}{\text{Distance of building top point from given point}}$

Explanation of Solution

Given information: 

Following figure is given:

  

Calculation:

As both triangles are similar, so ratios of their corresponding sides will be proportional, so,

  $\frac{\text{Height of lighthouse}}{\text{Height of building}}=\frac{\text{Distance of lighthouse from given point}}{\text{Distance of building from given point}}$

And another proportion that can be set, is:

  $\frac{\text{Height of lighthouse}}{\text{Height of building}}=\frac{\text{Distance of lighthouse top point from given point}}{\text{Distance of building top point from given point}}$

b)

To determine

To calculate: The height of the lighthouse.

Answer to Problem 12PPS

Height of the lighthouse is 200 ft.

Explanation of Solution

Given information: 

Following figure is given:

  

Concept used:

As both triangles are similar, so ratios of their corresponding sides will be proportional, so,

  $\frac{\text{Height of lighthouse}}{\text{Height of building}}=\frac{\text{Distance of lighthouse from given point}}{\text{Distance of building from given point}}$

Calculation:

On plug in all related given values given, in first proportion,

  $\begin{array}{c}\frac{x}{15}=\frac{120}{9}\\ x=\frac{120}{9}\times 15\\ =40\times 5\\ =200\end{array}$

By above calculation, the height of the lighthouse is 200 feet.