### Home > CCG > Chapter 11 > Lesson 11.1.5 > Problem11-77

11-77.

Hokiri’s ladder has two legs that are each $8$ feet long. When the ladder is opened safely and locked for use, the legs are $4$ feet apart on the ground. What is the angle that is formed at the top of the ladder where the legs meet?

Create a diagram of the ladder with a perpendicular bisector from the top ($∠C$) to the base (Segment $AB$).

Next, using the right triangle $ADC$ and a calculator, find the angle whose $\sin=\frac{2}{8}$.

$\text{sin}\left(\frac{\angle C}{2}\right)=\frac{2}{8}$ or $\frac{\angle C}{2}=\text{arcsin}\left(\frac{2}{8}\right)$

Since that will be half the angle, double the answer to get $∠C$.

$∠C=29°$