Question

If tan A=3/2, then the value of cos A is
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Answer 1

Step-by-step explanation:

$\tan( \alpha ) = \frac{3}{2} = \frac{perpendicular(p)}{base(b)} \\ \\ \\ let \: p = 3k \: and \: b = 2k \\ \\ h = \sqrt{ {p }^{2} + {b}^{2} } \\ h = \sqrt{ {(3k)}^{2} + {(2k)}^{2} } \\ h = \sqrt{9 {k}^{2} + {4k}^{2} } = \sqrt{13} k \\ \\ \\ \\ \cos( \alpha ) = \frac{base(b)}{hypotenus(h)} = \frac{2k}{ \sqrt{13}k } = \frac{2}{ \sqrt{13} }$