Solving for $\theta$ in a circle

Question

Let's say you have a pendulum hanging straight down and touching the ground at the lowest point. The pendulum has length $l$. If you pull the pendulum back so that the end is height $h$ above the ground, what degree does the pendulum make with the vertical in terms of $h$ and $l$?

(Question taken from a physics problem)

Answer 1

$AD=l,\hspace{15 pt} BD=h, \hspace{15 pt}\therefore AB=l-h $

In $\triangle ABC (\text{which is a right angle triangle}), AC=l$ and let $\angle CAB=\theta$

$\cos (\theta)=\large\frac{AB}{AC}=\frac{l-h}{l} \Rightarrow \theta= \cos^{-1}(\frac{l-h}{l})$

Answer 2

It is clear that projection of $\color{red}{l}$ on vertical line is $\color{red}{l\cos\theta}$. Now $$\color{blue}{h}+\color{red}{l\cos\theta}=l$$ This is now just an easy manipulation to get: $$\cos\theta=\frac{l-h}l\\\implies\theta=\cos^{-1}\left(\frac{l-h}l\right)\text{ or }\cos^{-1}\left(1-\frac hl\right)$$