Question

Given sin A =5/13 find the value of cos A and Tan A

Answer 1

Given,

$\bf \: Sin \: A \: = \frac{5}{13}$

We know that,

$\bf \: Sin \: \theta \: = \frac{Perpendicular}{Hypotenuse}$

So, Perpendicular = 5
Hypotenuse = 13

So,

${H}^{2} = {P}^{2} + {B}^{2} \\ \\ {(13)}^{2} = {(5)}^{2} + {(b)}^{2} \\ \\ {b}^{2} = 169 - 25 \\ \\ b = \sqrt{144} \\ \\ B = 12$

Now,

Since,

$\bf \: Cos \: \theta \: = \frac{Base}{Hypoenuse} \\ \\ \bf \: Tan \: \theta \: = \frac{Perpendicular}{Base}$

Putting the values,

$\bf \: Cos \: A = \frac{12}{13} \\ \\ \bf \: Tan \: A \: = \frac{5}{12}$

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