Question

If tan A = 3/2, then find the value of cos A​

Answer 1

Answer:

$\frac{2}{ \sqrt{13} }$

Step-by-step explanation:

$\tan(a) = \frac{3}{2} \\ \frac{p}{b} = \frac{3}{2} \: \: ( \frac{perpendicular}{base} ) \\ let \: p \: be \: 3x \: and \: b \: be \: 2x \\ by \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ h = \sqrt{ {(3x)}^{2} } + {(2x)}^{2} \\ h = \sqrt{9 {x}^{2} } + 4 {x}^{2} \\ h = \sqrt{13 {x}^{2} } \\ h = x \sqrt{13} \\ \\ now \: \cos(a) = \frac{b}{h} \\ = \frac{2x}{x \sqrt{13} } \\ = \frac{2}{ \sqrt{13}}$

Hope it helps!!