# How do you find the exact value of #tan(arcsin(1/3))#?

##### 1 Answer

Feb 9, 2017

#### Explanation:

Consider a right angled triangle with sides

We can tell that it is right angled since:

#1^2+(2sqrt(2))^2 = 1+8 = 9 = 3^2#

Denote the smallest internal angle by

Then:

#sin(theta) = "opposite"/"hypotenuse" = 1/3#

#tan(theta) = "opposite"/"adjacent" = 1/(2sqrt(2)) = sqrt(2)/4#