Trapezoid diagonal f calculator

This function calculates the diagonal f of a trapezoid using the lengths of the sides and an angle. For the calculation, enter the lengths of the two sides a and d and the angle α. Then click the 'Calculate' button

Caculate Diagonal f  Input Delete Entries Side length a Side length d Angle α Decimal places 0 1 2 3 4 6 8 10  Results Diagonale f

Formulas for calculating the diagonal f using angle

If the height is not known, the diagonal f can also be calculated using the angle α.

\(\displaystyle f =\sqrt{(a^2+d^2) - (2 · a · d · cos(α))} \)

calculating the diagonal f using sides and height

Use of the side length a and d

The diagonal f forms a right triangle with the height h and the side (a - x). The diagonal f that forms the hypotenuse here can be calculated according to the Pythagorean theorem.

First, the length of x has to be calculated, which in turn can be calculated from d and h :

\(\displaystyle x =\sqrt{d^2-h^2} \)

The diagonal f can now be calculated using the following formula:

\(\displaystyle f =\sqrt{(a-x)^2+h^2} \)

The formula above is also used by this online calculator.

Use of the side length c and b

Alternatively, you can calculate with the side lengths c and b . To do this, the leg of the right triangle is first calculated:

\(\displaystyle y =\sqrt{b^2-h^2} \)

In the following formula, y is added to the side length c .

\(\displaystyle f =\sqrt{(c+y)^2+h^2} \)