Chapter 12.5, Problem 4P

To determine

Find the distance of ladder (30 ft) long from the base of building which makes an angle of $75°$ with the ground.

Answer to Problem 4P

The distance of ladder from the base of building is $7.76\text{ ft}$ .

Explanation of Solution

Given information: The given ladder is 30 ft long and this ladder makes an angle of $75°$ with the ground.

Calculation: Consider that the height of the building is (BC) which is at a distance of (AB) from the base of ladder making an angle of $75°$ with the ground as shown in assumed triangle. Therefore by trigonometric ratio in triangle assumed below,

  

  $\begin{array}{c}\cos \left(\theta \right)=\frac{AB}{AC}\\ \cos \left(75\right)=\frac{AB}{30}\\ \text{or, }AB=\left(30\right)\cos \left(75\right)\\ AB=7.76\text{ ft}\end{array}$

Hence the distance of ladder from the base of building is $7.76\text{ ft}$ .