Chapter 9.8, Problem 22E

To determine

Tofind:Distance between bottom of ladder and building

Answer to Problem 22E

Approximately 6 ft

Explanation of Solution

Given information:

Length of ladder $=24\text{ft}$

Angle between ladder and ground $={75}^{\circ }$

Concept Used:

In a right-angled triangle ABC, sine for acute angle $\angle A$ is the ratio of length of side opposite to angle $\angle A$ to the length of hypotenuse and cosine of acute angle $\angle A$ is the ratio of length of side adjacent to angle $\angle A$ to the length of hypotenuse.

Calculation:

Distance betweenbuilding and bottom of ladder be $=x$

Basis definition we can say-

  $\begin{array}{l}\cos {75}^{\circ }=\frac{Adjacent}{Hypotenuse}\\ \Rightarrow 0.2588=\frac{x}{24}\\ \Rightarrow x=\left(0.2588\right)24\\ \Rightarrow x=6.2116\\ \Rightarrow x\approx 6\end{array}$

Distance betweenbuilding and bottom of ladder is approximately 6 ft