Free · Algebra and geometric relations

Right Triangle with Named Sides

Solve the sides and acute angles of a right triangle from sides, an angle or area.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked example, c = 5.

c²=a²+b²; A=ab/2; tan α=a/b

Worked example

Enter these known values and leave the other values blank.

Given
0
a
3 cm
b
4 cm
c
5 cm
Angle α
36.87 deg
Angle β
53.13 deg

Assumptions and limitations

  • Lengths and area are positive and acute angles lie between 0 and 90 degrees.
  • The area-and-hypotenuse inverse selects the larger leg; exchanging legs gives another valid triangle.

Common questions

How do I use this relation?

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

What do the displayed numbers mean?

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

References

Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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