Right Triangle Calculator
Please provide 2 values below to calculate the other values of a right triangle
If radians are selected as the angle unit, it can take values such as pi/3, pi/4, etc.
Right Triangle
A right triangle is a triangle in which one angle is a right angle (90°). The side opposite the right angle is called the hypotenuse (c), and the other two sides are called the legs (a and b). The angles opposite sides a and b are denoted as α (alpha) and β (beta), respectively.
The altitude (h) from the right angle vertex to the hypotenuse divides the triangle into two smaller right triangles that are similar to the original triangle.
Pythagorean Theorem: In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides:
Pythagorean Triple: A set of three positive integers that satisfy the Pythagorean theorem. Common examples include: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25; 20, 21, 29; and many others.
Area and Perimeter:
A = ½ab = ½ch
P = a + b + c
Special Right Triangles
30°-60°-90° Triangle
A special right triangle where the angles are 30°, 60°, and 90°. The sides are in the ratio 1:√3:2.
Properties:
- Angles: 30° : 60° : 90°
- Ratio of sides: 1 : √3 : 2
- Side lengths: a : b : c (where a is opposite 30°, b is opposite 60°, c is hypotenuse)
Example:
Given that the side corresponding to the 60° angle is 5:
b = 5 (60° side)
a = b/√3 = 5/√3 ≈ 2.887 (30° side)
c = b × 2/√3 = 10/√3 ≈ 5.774 (hypotenuse)
This triangle is useful for calculating trigonometric functions of multiples of π/6 (30°).
45°-45°-90° Triangle
An isosceles right triangle where the two legs are equal in length and the angles are 45°, 45°, and 90°. The sides are in the ratio 1:1:√2.
Properties:
- Angles: 45° : 45° : 90°
- Ratio of sides: 1 : 1 : √2
- Side lengths: a : a : c (where a = b, c is hypotenuse)
Example:
Given that the hypotenuse c = 5:
c = 5 (hypotenuse)
a = b = c/√2 = 5/√2 ≈ 3.536 (equal legs)
This triangle is useful for calculating trigonometric functions of multiples of π/4 (45°).