Question

In the given figure, find the values of $\cos \theta$ and $\tan \theta$

Answer 1

Given that:

$AB=5$ and $AC=13$

To find:

$\cos \theta =?$ and $\tan \theta =?$

Solution:;

By Pythagorean theorem,

$BC=\sqrt{A{C}^2-A{B}^2}$

$=\sqrt{{13}^2-5^2}$

$=\sqrt{169-25}$

$=\sqrt{144}$

$=12$

Now, $\cos \theta =\frac{BC}{AC}=\frac{12}{13}$

and $\tan \theta =\frac{AB}{BC}=\frac{5}{12}$