Question

In a right angle triangle $ABC$ with right angle at $B$, in which $a=24$ units, $b=25$ units and $\angle BAC=\theta$. Then, find $\cos \theta$ and $\tan \theta$.

Answer 1

From the figure,

$A{C}^2=A{B}^2+B{C}^2$

$A{B}^2={25}^2-{24}^2$

$AB=\sqrt{625-576}$

$AB=\sqrt{49}$

$AB=7cm$

Now,

$\cos \theta =\frac{AB}{AC}$

$=\frac{7}{25}$

$\tan \theta =\frac{BC}{AB}$

$=\frac{24}{7}$