Chapter 8.6, Problem 15WE

To determine

To find the distance from point $A$ on the of a lake to point $B$ on an island in lake.

Answer to Problem 15WE

  $AB=148.762m$

Explanation of Solution

Given information:

A surveyor locate point P with $m\angle PAB=65,m\angle APB=25\text{and}PA=352m.$

$$ From sine rule, $\sin \left({25}^{\circ }\right)=\frac{\text{perpendicular}}{\text{hypotenuse}}$

  $\begin{array}{l}\Rightarrow \text{perpendicular=}\sin \left({25}^{\circ }\right)\times 352\\ \therefore \text{perpendicular=}148.762m\end{array}$

Hence, $AB=148.762m$