Bibhorr Formula

Bibhorr formula yields a relation between three sides and angle of a right triangle. The angle which is equated to linear variables is the Bibhorr angle. The formula is a superior alternative to trigonometry as it is devoid of sine and cosine functions. The equation establishes a geometric construction among the elements of a triangle as opposed to trigonometry.

Statement

For a given right triangle with longest side श्र, medium side लं and shortest side छ, the angle opposite the medium side (Bibhorr angle) बि is given as:

Download.png

This equation is known as Bibhorr formula. The symbolical notations use Hindi letters and specifically denote the sides.

Constants

The use of two constants - $90^{\circ}$ or $\frac{\pi}{2}$ and $1.5$ makes the formula more legible. These constants are known as "Bibhorr sthiron" and "Bibhorr constant" respectively.

Units

The units of Bibhorr angle depend on the the units of Bibhorr sthiron. If this constants is $90^{\circ}$ then angle is in degrees but if Bibhorr sthiron is in the form $\frac{\pi}{2}$ then Bibhorr angle results in radians.

Explanation

Bibhorrformula.jpg

Consider a right triangle ABC, such that BC and AC are shortest and medium sides respectively and AB is the longest side or hypotenuse. Now, the angle opposite AC, called Bibhorr angle is given as:

Download.png

See also

Invalid username
Login to AoPS