Question

If sin tetha=5/17, what is the value of tan tetha

Answer 1

find the value of adjacent side(PYTHAGORES THEOREM)
then substitute u will get the valve

Answer 2

Given,

Sin theta = $\frac{5}{17}$

=> $\frac{p}{h}$ = $\frac{5}{17}$ = k (let)

=> p = 5k and h = 17k


Applying Pythagoras theorem

${h}^{2} = {p}^{2} + {b}^{2} \\ \\ = > ( {17k})^{2} = ( {5k})^{2} + {b}^{2} \\ \\ = > 289 {k}^{2} - 25 {k}^{2} = {b}^{2} \\ \\ = > 264 {k}^{2} = {b}^{2} \\ \\ = > b = \sqrt{264 {k}^{2} } \\ \\ = > b \: = \sqrt{264} \: \: \: k$
$tan \: theta = \frac{p}{b} \\ \\ = \frac{ {5k} }{ \sqrt{264} \: \: \: k } \\ \\ = \frac{5}{ \sqrt{264} }$


$\huge{answer = \frac{5}{ \sqrt{264} } }$