Question

Güven 15 cot A s. find sin A and Sec A.​

Answer 1

$\bold{Given,}$

$\bold{15cotA=8}$

$\bold{cotA = \frac{8}{5} }$

$\bold{=> tanA= \frac{15}{8} - - - ( \tan \: A = \frac{1}{ \cot \:A }) }$

We know that,

$\bold{\tan \theta = \frac{opposite \: side}{adjecent \: angle} }$

Consider the attached figure, triangleABC

Consider the attached figure, triangleABCFrom Pythagoras theorem,

$\bold{AC^2=AB^2+BC^2}$

$\small\bold{AC^2=8^2+15^2= {8}^{2} + 225 =289 }$

$\bold{AC=17}$

$\bold{\cos \: A \: \frac{adjecent}{hypoteneuse} }$

$\bold{\sec \: A= \frac{1}{ \cos \:A} = \frac{ \frac{1}{8} }{17} \frac{17}{8} }$

$\bold{\sin \: A = \frac{opposite \: side}{hypotenuse} = \frac{BC}{AC} = \frac{15}{17} }$