Triangle from given side a, c and angle beta, calculator and formula

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

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

Triangle Calculator

Input

Angle β

Side length a

Side length c

Decimal places

Result

Side length b

Angle α

Angle γ

Height

Perimeter

Area

Formulas for calculation

Side b

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

Angle α

\(\displaystyle α = acos\left(\frac{a^2-b^2-c^2}{-2·b· c} \right)\)

Angle γ

\(\displaystyle γ = 180°-β-α\)

Perimeter

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

Height

\(\displaystyle h = b· sin(γ)\)

Area

\(\displaystyle A = \frac{a·h}{2}\)

Calculate a triangle from a,c and β

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