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  4. Right Triangle Calculator

Right Triangle Calculator

Enter any two of a, b, c, α, β, altitude h, area, or perimeter to solve a right triangle completely.

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How it works

Right angle at C; c is the hypotenuse; α opposite a; β opposite b. Provide two values and compute the rest.

a²+b²=c² · A=½ab=½ch · h=ab/c · α+β=90°

When to use

Use this tool when you need to: try legs 3 and 4 (c=5, A=6, h=2.4), or c=5 with α=45° for an isosceles right triangle.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try legs 3 and 4 (c=5, A=6, h=2.4), or c=5 with α=45° for an isosceles right triangle.

Frequently asked questions

What is the Right Triangle Calculator?
Right angle at C; c is the hypotenuse; α opposite a; β opposite b. Provide two values and compute the rest.
How do I use the Right Triangle Calculator?
Enter the required values, then calculate. The Right Triangle Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Right Triangle Calculator use?
a²+b²=c² · A=½ab=½ch · h=ab/c · α+β=90°

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Right triangle calculator

Provide any two of sides a, b, hypotenuse c, acute angles α and β, altitude h to the hypotenuse, area, or perimeter. The calculator recovers every remaining measure of a right triangle (∠C = 90°).

Angle unit

Enter exactly two independent values (leave the rest blank). Side a is opposite α; side b is opposite β; c is the hypotenuse opposite the right angle at C.

Diagram appears after a successful solve (right angle at C, altitude dashed).

Angle unit: degrees. α and β are acute with α + β = 90°.

Try an example

How it works

What is a right triangle?

A right triangle has one angle of 90°. The side opposite that angle is the hypotenuse (c), the longest side. The other two sides are legs a and b. Acute angles α (opposite a) and β (opposite b) always sum to 90°. Integer-sided right triangles form Pythagorean triples such as 3-4-5, 5-12-13, and 8-15-17.

Area and perimeter

Area A = ½ab. The same area equals ½ch where h is the altitude from the right angle to the hypotenuse, so A = ½ch and h = ab/c = 2A/c. Perimeter P is simply a + b + c.

Special right triangles

30°-60°-90°: side opposite 30° : opposite 60° : hypotenuse = 1 : √3 : 2. Knowing one side fixes the others. 45°-45°-90° (isosceles right): legs equal, ratio leg : hyp = 1 : √2 (or both legs : hyp = 1 : 1 : √2). These ratios also evaluate trig for π/6 and π/4 multiples.

Altitude to the hypotenuse

The altitude from C to hypotenuse c creates two smaller right triangles similar to each other and to the original. It splits c into segments p = a²/c and q = b²/c with p + q = c, and h² = p·q.

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