Right Triangle Calculator

Unlock the secrets of right triangles! Enter any two values and calculate sides, angles, and trigonometric functions instantly.

Right Triangle Calculator

Enter two known values to calculate the remaining sides and angles of a right triangle.

Right Triangle

Right Triangle Results:

Side a:
Side b:
Hypotenuse c:
Angle A: °
Angle B: °
Angle C: 90° (Right Angle)

Trigonometric Functions Calculator

Calculate sine, cosine, tangent, cosecant, secant, and cotangent for a given angle.

Trigonometric Function Results:

sin(°):
cos(°):
tan(°):
cosec(°):
sec(°):
cot(°):

Understanding Right Triangles & Trigonometry

A right triangle is defined by having one angle that measures exactly 90 degrees. The longest side, opposite the right angle, is known as the hypotenuse (c). The other two sides are called legs (a and b).

Key Concepts

  • Pythagorean Theorem: In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Formula: a2 + b2 = c2.
  • Angles: The sum of angles in any triangle is 180°. In a right triangle, one angle is 90°, so the other two acute angles sum to 90°.
  • Trigonometric Functions: These functions relate the angles of a right triangle to the ratios of its sides. The primary functions are:
    • Sine (sin): Ratio of the length of the opposite side to the hypotenuse. sin(θ) = Opposite / Hypotenuse
    • Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse. cos(θ) = Adjacent / Hypotenuse
    • Tangent (tan): Ratio of the length of the opposite side to the adjacent side. tan(θ) = Opposite / Adjacent
  • Reciprocal Trigonometric Functions:
    • Cosecant (cosec): cosec(θ) = 1 / sin(θ)
    • Secant (sec): sec(θ) = 1 / cos(θ)
    • Cotangent (cot): cot(θ) = 1 / tan(θ)

How to Use This Calculator

Simply input two known values of your right triangle - these can be two side lengths, or one side length and one acute angle. The calculator will then determine the remaining sides and angles. For trigonometric functions, enter any angle in degrees to calculate the values of sin, cos, tan, cosec, sec, and cot for that angle. Use the 'Reset' button to clear inputs and start afresh.