Where A is the area, a and b are the sides' lengths, alpha is the angle at the common vertex.Īctually, this form directly follows from half of the base times height formula because the triangle's height would be. Side-angle-side formulaĪlso referred to as SAS, this formula allows you to find a triangle area if you know two sides and the angle at a common vertex (included angle). A proof can be found in his book Metrica written around 60 AD. The formula is named after Hero of Alexandria, a Greek Engineer and Mathematician, in 10 - 70 AD. Where A is the area, a, b, c are the lengths of the sides, p is the perimeter divided by 2 (semi-perimeter). You can find the area of a triangle if you know the lengths of all sides. Where A is the area, a is the length of the base, h is the altitude's length. Any side can be the base, but the altitude must correspond to the base. You can find the triangle area from the length of the base and the length of the corresponding altitude. You can find all formulas below the calculator. This formula is derived from Heron's formula and uses only the length of one side to calculate the area. This formula uses the coordinates of the vertices to find the length of the sides of the triangle and then uses Heron's formula to find the area.įinally, if you are dealing with an equilateral triangle, there is a simplified formula that can be used. If you know the coordinates of the three vertices of the triangle, you can use the Coordinates formula. This formula uses the two side lengths and the included angle to calculate the area of the triangle. If you know two sides and the included angle of the triangle, you can use the Side-angle-side formula to find the area. Heron's formula is useful when you do not know the height of the triangle or when the triangle is not a right triangle. This formula uses the three side lengths to calculate the semiperimeter, which is then used to find the area of the triangle. If you know all three sides of the triangle, you can use Heron's formula. This formula takes half of the base length and multiplies it by the altitude length to find the area. To find the third angle (angle C) you can apply the law that all triangles add up to 180 degrees.If you know the base and the altitude of the triangle, you can use the Half of base times height formula. Since two angle measures are already known, the third angle will be the simplest and quickest toĬalculate. Would begin solving the problem by determing with value to find first. If told to find the missing sides and angles of a triangle with angle A equaling 34 degrees, angle B equaling 58 degrees, and side a equaling a length of 16, you Solving Triangles Given Two Angles and One Side Just input one side length and any two other values, and our calculator will return missing values in exact value and decimal form in addition to the step-by-step calculation process for each of those missing values. The law of sines and law of cosines are essential to the calculation process. With an oblique triangle calculator, all values can be calculated if eitherġ side and any two other values are known. Oblique triangles use a set of formulas unique from right angle triangles. An oblique triangle is defined as any triangle without a right angle (90-degree angle).
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