# What is the Value of Tan 90 Degrees ?

## Solution :

The value of tan 90 degrees is $$\infty$$ or not defined.

Proof :

$$\angle$$ A of $$\Delta$$ ABC is made large and large until it becomes 90 degrees. As $$\angle$$ A gets large and large $$\angle$$ C gets smaller and smaller. Side AB goes on decreasing. The point A gets closer to point B. When $$\angle$$ C becomes very close to 0 degree. The side AC almost coincide with side BC and side AB becomes to zero.

So, AC = BC and AB = 0

By using trigonometric formulas,

$$tan 90^{\circ}$$ = $$perpendicular\over base$$ = $$p\over b$$

$$tan 90^{\circ}$$ = $$BC\over AB$$ = $$BC\over 0$$ = $$\infty$$ or not defined

Hence, the value of $$tan 90^{\circ}$$ = $$\infty$$ or not defined.