# What is the exact value of tan 45?

$\tan \left({45}^{\circ}\right) = 1$
A 45-45-90 triangle has legs of identical length and a hypotenuse of $\sqrt{2}$ times that.
By SOHCAHTOA, tangent is opposite over adjacent, which are the two legs. Since they have the same length, $\tan \left({45}^{\circ}\right) = 1$