Calculate Diagonals Angles
Calculator for the length and the angles of the diagonals in a rectangle. Both diagonals are the same length and have the same angles; they intersect in the middle. The length of a diagonal d is calculated using the Pythagorean theorem, where one of the diagonals is the hypotenuse of a right triangle and the two different sides of the rectangle are its legs. The angles in the corners of the rectangle are calculated with the law of cosines in a triangle with the sides a, b and d. The angles between the diagonals result from the angular sum in a triangle of 180 degrees and the values of the corner angles. Please enter length and width, the diagonal length and the angles will be calculated.
The formulas for calculating the length and angles of the diagonals are:
Diagonal, d = √ a² + b²
Angle alpha, α = acos[ ( b² + d² - a² ) / 2bd ]
Angle beta, β = acos[ ( a² + d² - b² ) / 2ad ]
Angle gamma, γ = 180° - 2β
Angle delta, δ = 180° - 2α
acos is the arccosine, i.e. the inverse function of the cosine. Here you can convert degrees into radian and into degrees,minutes and seconds.
Example: a rectangle with sides 3 and 4 has a diagonal length of 5. These three values are the best known examples of a Pythagorean triple, a right-angled triangle with integer side lengths. In this rectangle, the right angles are divided into α = 36.87 degrees and β = 53.13 degrees. The two intersection angles of the diagonals, which add up to 180 degrees, are γ = 73.74 degrees and δ = 106.26 degrees. In contrast to the rectangle drawn here, this rectangle is upright, so the short sides are at the top and bottom, and the long sides are left and right. The angle gamma is acute and delta is obtuse.