Question:
In Fig. $5.48, A D=4 \mathrm{~cm}, B D=3 \mathrm{~cm}$ and $C B=12 \mathrm{~cm}$, find the $\cot \theta$.
(a) $\frac{12}{5}$
(b) $\frac{5}{12}$
(C) $\frac{13}{12}$
(d) $\frac{12}{13}$
Solution:
We have the following given data in the figure, $A D=4 \mathrm{~cm}, B D=3 \mathrm{~cm}, C B=12 \mathrm{~cm}$
Now we will use Pythagoras theorem in $\triangle A B D$,
$A B=\sqrt{3^{2}+4^{2}}$
$=5 \mathrm{~cm}$
Therefore,
$\cot \theta=\frac{C B}{A B}$
$=\frac{12}{5}$
So the answer is $(a)$