Question

If $5sec\theta =13$ then prove that $sin\theta =\frac{12}{13}$

Answer 1

Using pythagoras theorem,

$\left({AB}^2\right)=\left({AC}^2\right)+\left({BC}^2\right)$

$AB=\sqrt{{13}^2-5^2}$

$AB=\sqrt{169-25}$

$AB=\sqrt{144}$

$AB=12cm$

$\sin \theta =\frac{opp}{hyp}$

$\sin \theta =\frac{12}{13}$