Chapter 9.10, Problem 18PSC

To determine

To find:The value of height PB

Answer to Problem 18PSC

The value of height $PB=3.29\text{ km}$

Explanation of Solution

Given information:The following information has been given

The elevation at point A is ${30}^0$

The elevation at point C is ${35}^0$

The distance between A and C is $1\text{ km}$

Formula used:Basic tangent definition has been used

Calculation:Let us assume the distance AB to be x and the distance CB to be y . hence, now we can find x and y as

  $\tan {30}^0=\frac{PB}{x}\to x=\frac{PB}{\tan {30}^0}$

  $\tan {35}^0=\frac{PB}{y}\to y=\frac{PB}{\tan {35}^0}$

  $x-y=1\text{ km}$

Thus, we get

  $\frac{PB}{\tan {30}^0}-\frac{PB}{\tan {35}^0}=1$

Hence, solving the linear equation, we get

  $PB=3.29\text{ km}$