Triangle calculator

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

You have entered side a, c and angle γ.

Right scalene triangle.

Sides: a = 828   b = 2974.922184771   c = 3088

Area: T = 1231617.645495
Perimeter: p = 6890.922184771
Semiperimeter: s = 3445.461092386

Angle ∠ A = α = 15.55333016278° = 15°33'12″ = 0.2711456323 rad
Angle ∠ B = β = 74.44766983722° = 74°26'48″ = 1.29993400038 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 2974.922184771
Height: hb = 828
Height: hc = 797.6879821861

Median: ma = 3003.591051803
Median: mb = 1702.388773492
Median: mc = 1544

Inradius: r = 357.4610923857
Circumradius: R = 1544

Vertex coordinates: A[3088; 0] B[0; 0] C[222.0165544041; 797.6879821861]
Centroid: CG[1103.339851468; 265.8933273954]
Coordinates of the circumscribed circle: U[1544; -0]
Coordinates of the inscribed circle: I[470.5399076143; 357.4610923857]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.4476698372° = 164°26'48″ = 0.2711456323 rad
∠ B' = β' = 105.5533301628° = 105°33'12″ = 1.29993400038 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 828 ; ; b = 2974.92 ; ; c = 3088 ; ;

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

p = a+b+c = 828+2974.92+3088 = 6890.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6890.92 }{ 2 } = 3445.46 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3445.46 * (3445.46-828)(3445.46-2974.92)(3445.46-3088) } ; ; T = sqrt{ 1.517 * 10**{ 12 } } = 1231617.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1231617.64 }{ 828 } = 2974.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1231617.64 }{ 2974.92 } = 828 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1231617.64 }{ 3088 } = 797.68 ; ;

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{ 828**2-2974.92**2-3088**2 }{ 2 * 2974.92 * 3088 } ) = 15° 33'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2974.92**2-828**2-3088**2 }{ 2 * 828 * 3088 } ) = 74° 26'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3088**2-828**2-2974.92**2 }{ 2 * 2974.92 * 828 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1231617.64 }{ 3445.46 } = 357.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 828 }{ 2 * sin 15° 33'12" } = 1544 ; ;




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