# Suppose in a right triangle, cos(t)=3/4. How do you find: Sin(t)?

Oct 6, 2015

$\sin \left(t\right) = \frac{\sqrt{7}}{4}$

#### Explanation:

If $\cos \left(t\right) = \frac{3}{4}$
then a triangle with a hypotenuse of length $4$
in standard position ($\angle t$ at origin and adjacent side along positive X-axis)
would have an opposite side with a length of $\sqrt{{4}^{2} - {3}^{2}} = \sqrt{7}$
(based on Pythagorean Theorem)

$\sin = \left(\text{opposite")/("hypotenuse}\right)$

So $\sin \left(t\right) = \frac{\sqrt{7}}{4}$