Question

Refer to the triangle given in the figure.

If $\cos A$ is equal to $\frac{m}{5}$, find $m$.

Answer 1

Given, $△ABC$, perpendicular from B on AC, let it cut AC at D, such that$\angle BDA=\angle BDC={90}^{\circ }$
$AD=3$
$BD=4$
$BC=12$
In $△ABD$,
$A{B}^2=B{D}^2+A{D}^2$
$A{B}^2=3^2+4^2$
$AB=5$
In $△BCD$
$B{C}^2=C{D}^2+B{D}^2$
${12}^2=C{D}^2+4^2$
$C{D}^2=128$
$CD=8\sqrt{2}$
Now, $\cos A=\frac{B}{H}=\frac{AD}{AB}=\frac{3}{5}$
Therefore, $m$ is $3$.