Obtuse Triangle Calculator

An obtuse triangle features one internal angle greater than 90 degrees, while its remaining two angles are strictly acute. The fundamental rule governing all triangles dictates that the sum of all internal angles always equals 180 degrees: angle_one + angle_two + angle_three = 180. To find the area, depending on your known variables, the calculator utilizes standard formulas such as the base-height formula (0.5 * base * height), the side-angle-side sine method (0.5 * a * b * sin(angle)), or Heron's formula using all three known side lengths.

Let us walk through finding the area of an obtuse triangle using two side lengths and the included obtuse angle. Suppose you have a triangle where side a = 10 cm, side b = 6 cm, and the included angle is 120 degrees. First, convert the angle to radians or apply the sine formula directly: Area = 0.5 * a * b * sin(angle). Substituting our values, we get Area = 0.5 * 10 * 6 * sin(120°). Since sin(120°) is approximately 0.866, the calculation becomes 30 * 0.866, yielding a final area of approximately 25.98 square centimeters.

Always verify that your angle inputs accurately reflect a valid triangle before calculating. Remember that the longest side of an obtuse triangle is always opposite the obtuse angle. When measuring real-world objects or drafting blueprints, double-check your unit consistency—mixing centimeters and inches will distort your final area and angle computations.