Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, c and angle β.

Obtuse scalene triangle.

Sides: a = 74   b = 107.5865992753   c = 47

Area: T = 1441.696633867
Perimeter: p = 228.5865992753
Semiperimeter: s = 114.2932996376

Angle ∠ A = α = 34.76662786953° = 34°45'59″ = 0.60767860319 rad
Angle ∠ B = β = 124° = 2.16442082725 rad
Angle ∠ C = γ = 21.23437213047° = 21°14'1″ = 0.37105983492 rad

Height: ha = 38.96547659101
Height: hb = 26.80108186157
Height: hc = 61.34987803691

Median: ma = 74.31660340591
Median: mb = 30.8032817093
Median: mc = 89.29223452389

Inradius: r = 12.61440392184
Circumradius: R = 64.88660777328

Vertex coordinates: A[47; 0] B[0; 0] C[-41.38802748568; 61.34987803691]
Centroid: CG[1.87332417144; 20.45495934564]
Coordinates of the circumscribed circle: U[23.5; 60.48110142404]
Coordinates of the inscribed circle: I[6.70770036237; 12.61440392184]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2343721305° = 145°14'1″ = 0.60767860319 rad
∠ B' = β' = 56° = 2.16442082725 rad
∠ C' = γ' = 158.7666278695° = 158°45'59″ = 0.37105983492 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 74 ; ; b = 107.59 ; ; c = 47 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 74+107.59+47 = 228.59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 228.59 }{ 2 } = 114.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 114.29 * (114.29-74)(114.29-107.59)(114.29-47) } ; ; T = sqrt{ 2078488.33 } = 1441.7 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1441.7 }{ 74 } = 38.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1441.7 }{ 107.59 } = 26.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1441.7 }{ 47 } = 61.35 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 74**2-107.59**2-47**2 }{ 2 * 107.59 * 47 } ) = 34° 45'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 107.59**2-74**2-47**2 }{ 2 * 74 * 47 } ) = 124° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 47**2-74**2-107.59**2 }{ 2 * 107.59 * 74 } ) = 21° 14'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1441.7 }{ 114.29 } = 12.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 74 }{ 2 * sin 34° 45'59" } = 64.89 ; ;




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