Calculator and formulas for calculating the diagonal f of a trapezoid using angle
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
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If the height is not known, the diagonal f can also be calculated using the angle α.
\(\displaystyle f =\sqrt{(a^2+d^2) - (2 · a · d · cos(α))} \)
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.
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 .
\(\displaystyle f =\sqrt{(c+y)^2+h^2} \)
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