How to Compute Area of Triangle (angle side angle)

There are various ways to calculate the area of a triangle if you know side lengths and angle measures. The two most common formulas used to find the area of a triangle require either 3 sides lengths, or 2 side lengths and an angle.

This articlw will demonstrate a third way, the "angle side angle" method. You can use this formula if you know the length of one side, and the measures of the two adjacent angles.

Instructions

1. 

   To explain the method, let's use a triangle with a side length of 9 and two adjacent angles of 40 and 45 degrees. The first step is to square 9 and divide by 2. So (9)(9) = 81 and 81/2 = 40.5.

2. The next step in calculating the area is to take the number you found in step one and multiply it by the sines of 40 degrees and 45 degrees. Sine(40) = .6428, and sine(45) = .7071. And so (40.5)(.6428)(.7071) = 18.4082.

3. Next, use a calculator or trig table to find sine(40+45) = sine(85) = .9962. Now divide the number you got in step 2 by sine(85). 18.4082/.9962 = about 18.5. So the area of the triangle is 18.5 square units.

4. If you have a side length of A and two adjacent angles of x and y degrees, the general formula for the area of a triangle is [(1/2)A²sine(x)sine(y)]/sine(x+y).