Triangle from given side b,c and angle alpha, calculator and formula

With this calculator, the side length a, the angles β and γ, the area, height and the perimeter of a triangle is calculated from the side lengths b, c and the angle α

Enter the 3 values, then click on the 'Calculate' button.

Triangle calculator

Input

Angle α

Side length b

Side length c

Decimal places

Resultat

Side a

Angle β

Angle γ

Height

Perimeter

Area

Formulas for calculation

Side a

\(\displaystyle a = \sqrt{b^2+c^2-2bc·cos(α)} \)

Angle β

\(\displaystyle β = acos\left(\frac{a^2+c^2-b^2}{2ac} \right)\)

Angle γ

\(\displaystyle γ = acos\left(\frac{a^2+b^2-c^2}{2ab} \right)\)

Perimeter

\(\displaystyle P = a+b+c\)

Height

\(\displaystyle h = b· sin(γ)\)

Area

\(\displaystyle A = \frac{a·h}{2}\)

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