Formula for the Area of a Triangle

The area of a triangle iswhereis the base andis the perpendicular height. This formula is a bit artififical because we can take any side as the base and the height will be the perendicular distance of the opposite vertex from this chosen base.

There is another very useful formula,whereandare two sides andis the angle between them. This formula can be derived from the triangle above.

Make a right angled triangle as below and label the anglesandand the side

Using simple trigonometry for the right angled triangle gives

Use the identitysoand

Then