Finding out the missing side or angle couldn't be easier than with our great tool - right triangle side and angle calculator. Choose two given values, type them into the calculator and the remaining unknowns will be determined in a blink of an eye! If you are wondering how to find the missing side of a right triangle, keep scrolling and you'll find the formulas behind our calculator.

How to find the sides of a right triangle

There are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to find the missing side:

  1. Given two sides

If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:

a² + b² = c²

  • if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root:

    a = √(c² - b²)

  • if leg b is unknown, then

    b = √(c² - a²)

  • for hypotenuse c missing, the formula is

    c = √(a² + b)²

  1. Given angle and hypotenuse

Apply the law of sines or trigonometry to find the right triangle side lengths:

  • a = c * sin(α) or a = c * cos(β)

  • b = c * sin(β) or b = c * cos(α)

  1. Given angle and one leg

Find the missing leg using trigonometric functions:

  • a = b * tan(α)

  • b = a * tan(β)

  1. Given area and one leg

As we remember from basic triangle area formula, we can calculate the area by multiplying triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the height when the second leg is the base, so the equation gets simplified to:

area = a * b / 2

For example, if we know only the right triangle area and the length of the leg a, we can derive the equation for other sides:

  • b = 2 * area / a
  • c = √(a² + (2 * area / a)²)

How to find the angle of a right triangle

If you know one angle apart from the right angle, calculation of the third one is a piece of cake:

Givenβ: α = 90 - β

Givenα: β = 90 - α

However, if only two sides of a triangle are given, finding the angles of a right triangle requires applying some basic trigonometric functions:

for α

  • sin(α) = a / c so α = arcsin(a / c) (inverse sine)
  • cos(α) = b / c so α = arctan(b / c) (inverse cosine)
  • tan(α) = a / b so α = arctan(a / b) (inverse tangent)
  • cot(α) = b / a so α = arctan(b / a) (inverse cotangent)

and for β

  • sin(β) = b / c so α = arcsin(b / c) (inverse sine)
  • cos(β) = a / c so α = arctan(a / c) (inverse cosine)
  • tan(β) = b / a so α = arctan(b / a) (inverse tangent)
  • cot(β) = a / b so α = arctan(a / b) (inverse cotangent)

How to find the missing side of a right triangle? How to find the angle? Example

Let's show how to find the sides of a right triangle with this tool:

  1. Assume we want to find the missing side given area and one side. Select the proper option from a drop-down list. It's the third one.
  2. Type in the given values. For example, an area of a right triangle is equal to 28 in² and b = 9 in.
  3. Our right triangle side and angle calculator displays missing sides and angles! Now we know that:
  • a = 6.222 in
  • c = 10.941 in
  • α = 34.66°
  • β = 55.34°
Hanna Pamuła, PhD student

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Right Triangle Side and Angle. Calculator | Formula