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) = [tex] \frac{7}{10} [/tex]
We can find cos(x) as by identity which is given as below:
[tex]cos(x) = \sqrt{1 - (sin(x))^2} [/tex]
= [tex] \sqrt{1 - ( \frac{7}{10})^2 } [/tex]
= [tex] \sqrt{ \frac{100 - 49}{100} } = \sqrt{ \frac{51}{100} } [/tex]
= [tex]= \frac{ \sqrt{51} }{10} [/tex]
So cos(x) = [tex] \frac{ \sqrt{51} }{10} [/tex]
As we know
[tex]tan(x) = \frac{sin(x)}{cos(x)} [/tex]
= [tex] \frac{ \frac{7}{10} }{ \frac{ \sqrt{51} }{10} } [/tex]
[tex]= \frac{7}{ \sqrt{51} } [/tex]
So tan(x) = [tex] \frac{7}{ \sqrt{51} } [/tex]
