Chapter 8.6, Problem 14WE

To determine

To find the length of the wire

Answer to Problem 14WE

Length of the wire is $82.7533m$

Explanation of Solution

Given information:

A guy wire is attached to the top of a $75m$ tower and meets the ground at a $65{}^{\circ }$ angle.

It can be observed that the wire and tower forms a right angle triangle.

$$ From sine rule, $\sin \left({65}^{\circ }\right)=\frac{\text{perpendicular}}{\text{hypotenuse}}$

  $\begin{array}{l}\Rightarrow 0.9063=\frac{75}{\text{hypotenuse}}\\ \Rightarrow \text{hypotenuse}=\frac{75}{\left(0.9063\right)}\\ \therefore \text{hypotenuse}=82.7533m\end{array}$

Hence, length of the wire is $82.7533m$