Based on the diagram above, the area of can be found using any of the three formulas below.
Because is a right triangle, the height of the triangle can be related to the sine of using the sine ratio. Finally, substitute the expression found for into the general formula for finding the area of a triangle.
To obtain the second formula, notice that is also a right triangle and then, the sine ratio can be applied. Substituting this expression into the general formula for finding the area of a triangle gives the first formula.
To deduce the third formula, it is needed to draw the height from or
In this case, the length of the base is and the height is Since is a right triangle, the sine ratio can be used. Lastly, substitute the expression for into the formula to find the area of