Chapter 15.2, Problem 61E

To determine

To find: The distance between the houses.

Answer to Problem 61E

The distance between the houses is $214\cdot 9\text{meters}$ .

Explanation of Solution

Given information:

The distance between surveying crew and the houses is $319\text{meter}$ and $253\text{meter}$ .

Calculation:

Let the surveying crew be denoted by $C$ , and the two houses are denoted by $A$ and $B$ .

Let the distance between two houses be $C$ .

Let the distance between surveying crew and the houses $A$ is $b$ .

  $b=319$

Let the distance between surveying crew and the houses $B$ is $a$ .

  $a=253$

The angle subtended by two houses at the observing crew is $42°12\text{'}$ .

Calculate the angle in degree.

  $1°=60\text{'}$

Using above equation.

  $12\text{'}=0\cdot 2°$

So, $42°12\text{'}=42\cdot 2°$

Calculate the distance between the houses.

  $\begin{array}{c}{c}^2=a^2+b^2-2ab\cos C\\ ={253}^2+{319}^2-2\left(253\right)\left(319\right)\cos 42\cdot 2°\\ =101761+64009-2\left(253\right)\left(319\right)0\cdot 7408\\ =46194.5\end{array}$

  $\begin{array}{c}{c}^2=46194.5\\ c=\sqrt{46194.5}\\ =214\cdot 9\end{array}$

Therefore, the distance between the houses is $214\cdot 9\text{meters}$ .