how to find the sides of a right triangle

Right Triangle Calculator

Please provide ii values beneath to calculate the other values of a right triangle. If radians are selected as the angle unit of measurement, information technology tin accept values such as pi/3, pi/4, etc.

Right triangle

A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry.

In a right triangle, the side that is opposite of the ninety° angle is the longest side of the triangle, and is called the hypotenuse. The sides of a right triangle are ordinarily 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. 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 bending C (for a right triangle this volition be 90°) for side c, every bit shown below. In this calculator, the Greek symbols α (blastoff) and β (beta) are used for the unknown angle measures. h refers to the altitude of the triangle, which is the length from the vertex of the right bending of the triangle to the hypotenuse of the triangle. The altitude divides the original triangle into two smaller, similar triangles that are also like to the original triangle.

If all 3 sides of a right triangle have lengths that are integers, it is known as a Pythagorean triangle. In a triangle of this type, the lengths of the three sides are collectively known as a Pythagorean triple. Examples include: 3, 4, 5; v, 12, xiii; 8, 15, 17, etc.

Expanse and perimeter of a right triangle are calculated in the same manner as whatever other triangle. The perimeter is the sum of the three sides of the triangle and the expanse can exist adamant using the following equation:

Special Right Triangles

xxx°-60°-ninety° triangle:

The 30°-60°-90° refers to the angle measurements in degrees of this type of special right triangle. In this type of correct triangle, the sides respective to the angles 30°-lx°-90° follow a ratio of ane:√3:2. Thus, in this type of triangle, if the length of one side and the side's respective bending is known, the length of the other sides can be adamant using the above ratio. For case, given that the side corresponding to the 60° angle is 5, allow a be the length of the side corresponding to the 30° angle, b be the length of the lx° side, and c be the length of the 90° side.:

Angles: 30°: 60°: 90°

Ratio of sides: 1:√three:ii

Side lengths: a:5:c

Then using the known ratios of the sides of this special type of triangle:

Every bit tin be seen from the above, knowing merely one side of a xxx°-60°-90° triangle enables you to determine the length of whatever of the other sides relatively hands. This blazon of triangle can be used to evaluate trigonometric functions for multiples of π/vi.

45°-45°-xc° triangle:

The 45°-45°-90° triangle, also referred to equally 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:i:√2. Like the 30°-60°-90° triangle, knowing i side length allows you to make up one's mind the lengths of the other sides of a 45°-45°-90° triangle.

Angles: 45°: 45°: 90°

Ratio of sides: 1:one:√two

Side lengths: a:a:c

Given c= 5:

45°-45°-90° triangles can be used to evaluate trigonometric functions for multiples of π/4.

Source: https://www.calculator.net/right-triangle-calculator.html

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