Using Sine to Calculate the Area of a Triangle - Concept

We can use sine to calculate the area of any triangle. It doesn't have to be a right triangle so let's say if I knew an angle c and the 2 sides that were adjacent to it. How would I calculate the area? Well to do that we're going to have to go back way back to the beginning of Geometry, when we said that the area of a triangle is its base times its height divided by 2. Well we can see that if I dropped and altitude down right here and if I called that my height h, we can see that our base is actually a in terms of this drawing and our height well we're going to have to use trigonometry to find our height.
If I look at angle c which apparently is the only that I know, if I look at the opposite and hypotenuses that's going to be sine. So I could say that the sine of angle c is equal to our height divided by the hypotenuse of this right triangle which is b. So if I want to solve for h because again I want to substitute in here b and h I would multiply both sides by the variable b. So b divided by b is 1 so we get our height is equal to b times the sine of the angle c. So substituting in b times the sine of c for h and a for b into this equation we're going to find that the area of this triangle is a times b times the sine of c all divided by 2. So if you want to calculate the area of any triangle and you don't know the height all you're needed to know is 1 angle and 2 included sides and you can use this formula a times b times the sine of c divided by 2.