Question

A 13-foot long ladder is placed against a wall and then the base of the ladder is pulled away from the wall. As the base of the ladder is pulled away from the wall, the top of the ladder slides down the wall (and the length of the ladder stays fixed).Let x represent the distance (in feet) from the base of the ladder to the wall, and let θ represent the radian measure of the angle the ladder forms with the ground.Suppose the base of the ladder is 9 feet from the wall (x=9). What is the value of θ?θ=Write a formula that expresses θ in terms of x.θ=

Answer 1

According to the given data

A right angled triangle can be formed with ladder as its hypotenus.

From the triangle in the above image,

$\begin{gathered} \cos \theta=\frac{Base}{Hypotenus} \\ \cos \theta=\frac{9}{13} \\ \theta=\cos ^{-1}(\frac{9}{13}) \end{gathered}$