Question

A 12-foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground. What is the angle formed by the ground and the ladder?

Short answer

The angle is $\begin{array}{rcl}& & 61.045°\end{array}$approximately.

Step-by-step solution

Step 1. Given Information

The height of the top of the ladder is 10.5 feet and the length of the ladder is 12 feet.

Step 2. Use the rule of Sines

• According to the rule of sines, $\frac{\sin A}{a}=\frac{\sin B}{b}$.
• Here, the angle of the building with the ground will be $90°$.
• Substitute $A=90°,a=12,b=10.5$and solve for B.

$\begin{array}{rcl}\frac{\sin 90°}{12}& =& \frac{\sin B}{10.5}\\ \sin B& =& \frac{10.5}{12}\\ & =& 0.875\\ B& \approx & 61.045°\end{array}$