how is sin a = perpendicular by base

Ans:
Hello Student,
Please find answer to your question below

First what you have written is wrong.


Well there is no particular reason behind this.
You can understand in this way.
tan(a) is defined as a slope.
Lets assume a point P(x, y) in the coordinate plane.
Join this point to origin O(0, 0).
Now, slope of OP is

Projection of OP on x-axis is x. Lets point A (x, 0)
Now we have triangle OAP, in which


By Definition, we have

From here, we have