The area of the triangle is half the product of its base and altitude. In the figure below for instance, the area of the two triangles with base and altitude is given by the formula .

In this post, we derive the area of a triangle using trigonometry In particular, we want to compute for the area of triangle given angle and side .

Given and side , we can compute for the altitude since

.

Simplifying, we have

.

Now, since area is the product of its base and its height,

.

.

From this derivation, it also follows that

and

.

Also a good spot to show the relations of .

Yes, that’s actually true.