Question

Let x represent the measure of an acute angle of a right triangle. suppose that sin (x) = 7⁄10 . find tan (x) and cos (x).

Answer 1

x represent an acute angle. So x < 90. So it means it is in first quadrant. So value of cos (x) and tan (x) are positive.

Sin(x) = $\frac{7}{10}$

We can find cos(x) as by identity which is given as below:

$cos(x) = \sqrt{1 - (sin(x))^2}$
                  = $\sqrt{1 - ( \frac{7}{10})^2 }$
                  = $\sqrt{ \frac{100 - 49}{100} } = \sqrt{ \frac{51}{100} }$
                  = $= \frac{ \sqrt{51} }{10}$
So cos(x) = $\frac{ \sqrt{51} }{10}$
 
 As we know 
$tan(x) = \frac{sin(x)}{cos(x)}$
                 = $\frac{ \frac{7}{10} }{ \frac{ \sqrt{51} }{10} }$
                 $= \frac{7}{ \sqrt{51} }$

So tan(x) = $\frac{7}{ \sqrt{51} }$