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 trinagle 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.

Difficulty: Easy

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).