Simple approximation to solve an oblique triangle

The previous post gave a simple and accurate approximation for the smaller angle of a right triangle. Given a right triangle with sides a, b, and c, where a is the shortest side and c is the hypotenuse, the angle opposite side a is approximately in radians. The previous post worked in degrees, but here we’ll use radians. If the triangle is oblique rather than a right triangle, there an approximation for the angle A that doesn’t require inverse trig functions, though it does require square roots. The approximation is derived in [1] using the same series that is the basis of the approximation in the earlier post, the power series for 2 csc(x) + cot(x). For an oblique triangle, the approximation is where s is the semiperimeter. For comparison, we can find the exact value of A using the law of cosines. and so Here’s a little Python script to see how accurate the approximation is. from math import sqrt, acos def approx(a, b, c): "approximate the angle opposite a" s = (a + b + c)/2 return…