Chapter 12.6, Problem 10P

To determine

To determine the angle at which roof is incline to the horizontal.

Answer to Problem 10P

The angle between roof and horizontal is ${34.2}^{\circ }$

Explanation of Solution

Given information :

Flagpole is 4m

Wire is 5m

Roof is 6m

We shall draw the diagram for given situation.

  

Here we shall use the cosine rule.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

First we have to determine angle B, then subtract the result from ${90}^{\circ }$ to get the angle between roof and horizontal.

Put the values, we get,

  $\begin{array}{l}\cos B=\frac{{\left(6\right)}^2+{\left(4\right)}^2-5^2}{2\left(6\right)\left(4\right)}\\ \cos B=\frac{27}{48}\\ B={\cos }^{-1}0.5625\\ B={55.8}^{\circ }\end{array}$

The angle between roof and horizontal is ${90}^{\circ }-55.8={34.2}^{\circ }$