Question

what is the square foot of a triangle that is 20x21x31feet ?

Answer 1

If you mean the area in square feet, then first we need to find one angle, using the cosine rule.

Let’s pick the largest angle opposite the longest side:

31²=20²+21²-2(20)(21)cos(x) where x is the largest angle.

So 961=400+441-840cos(x), 840cos(x)=841-961=-120. So cos(x)=-120/840=-1/7.

We need sin(x)=√(1-(-1/7)²)=√(1-1/49)=√48/7=4√3/7

The area of the triangle in square feet is ½(20)(21)sin(x)=840√3/7=120√3=207.846 sq ft approx.