The sides of the triangle are 5.2, 4.6, and x.

The second stage is the calculation of the properties of the triangle from the available lengths of its three sides.Īn isosceles triangular frame has a measure of 72 meters on its legs and 18 meters on its base.

From the known height and angle, the adjacent side, etc., can be calculated.Ĭalculator use knowledge, e.g., formulas and relations like the Pythagorean theorem, Sine theorem, Cosine theorem, and Heron's formula. Calculator iterates until the triangle has calculated all three sides.įor example, the appropriate height is calculated from the given area of the triangle and the corresponding side. These are successively applied and combined, and the triangle parameters calculate. He gradually applies the knowledge base to the entered data, which is represented in particular by the relationships between individual triangle parameters. The calculator tries to calculate the sizes of three sides of the triangle from the entered data.

The expert phase is different for different tasks.

How does this calculator solve a triangle?The calculation of the general triangle has two phases: Usually by the length of three sides (SSS), side-angle-side, or angle-side-angle. Of course, our calculator solves triangles from combinations of main and derived properties such as area, perimeter, heights, medians, etc. The classic trigonometry problem is to specify three of these six characteristics and find the other three. Each triangle has six main characteristics: three sides a, b, c, and three angles (α, β, γ).

Like the 30°-60°-90° triangle, knowing one side length allows you to determine the lengths of the other sides of a 45°-45°-90° triangle.Ĥ5°-45°-90° triangles can be used to evaluate trigonometric functions for multiples of π/4.The calculator solves the triangle specified by three of its properties. The 45°-45°-90° triangle, also referred to as an isosceles right triangle, since it has two sides of equal lengths, is a right triangle in which the sides corresponding to the angles, 45°-45°-90°, follow a ratio of 1:1:√ 2. This type of triangle can be used to evaluate trigonometric functions for multiples of π/6. Then using the known ratios of the sides of this special type of triangle: a =Īs can be seen from the above, knowing just one side of a 30°-60°-90° triangle enables you to determine the length of any of the other sides relatively easily. For example, given that the side corresponding to the 60° angle is 5, let a be the length of the side corresponding to the 30° angle, b be the length of the 60° side, and c be the length of the 90° side.: Thus, in this type of triangle, if the length of one side and the side's corresponding angle is known, the length of the other sides can be determined using the above ratio. In this type of right triangle, the sides corresponding to the angles 30°-60°-90° follow a ratio of 1:√ 3:2. The 30°-60°-90° refers to the angle measurements in degrees of this type of special right triangle. The perimeter is the sum of the three sides of the triangle and the area can be determined using the following equation: A = Examples include: 3, 4, 5 5, 12, 13 8, 15, 17, etc.Īrea and perimeter of a right triangle are calculated in the same way as any other triangle. In a triangle of this type, the lengths of the three sides are collectively known as a Pythagorean triple. If all three sides of a right triangle have lengths that are integers, it is known as a Pythagorean triangle. The altitude divides the original triangle into two smaller, similar triangles that are also similar to the original triangle. h refers to the altitude of the triangle, which is the length from the vertex of the right angle of the triangle to the hypotenuse of the triangle. In this calculator, the Greek symbols α (alpha) and β (beta) are used for the unknown angle measures.

Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90°) for side c, as shown below.

The sides of a right triangle are commonly referred to with the variables a, b, and c, where c is the hypotenuse and a and b are the lengths of the shorter sides. In a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry. Related Triangle Calculator | Pythagorean Theorem Calculator Right triangleĪ right triangle is a type of triangle that has one angle that measures 90°.

Isosceles triangle formula angles