Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 63   b = 86   c = 87

Area: T = 2537.337718689
Perimeter: p = 236
Semiperimeter: s = 118

Angle ∠ A = α = 42.70771248167° = 42°42'26″ = 0.74553799421 rad
Angle ∠ B = β = 67.79993830025° = 67°47'58″ = 1.18333224642 rad
Angle ∠ C = γ = 69.49334921808° = 69°29'37″ = 1.21328902473 rad

Height: ha = 80.55503868856
Height: hb = 59.00878415557
Height: hc = 58.33295905033

Median: ma = 80.56220878578
Median: mb = 62.610990337
Median: mc = 61.56550062942

Inradius: r = 21.50328575161
Circumradius: R = 46.44329799116

Vertex coordinates: A[87; 0] B[0; 0] C[23.80545977011; 58.33295905033]
Centroid: CG[36.93548659004; 19.44331968344]
Coordinates of the circumscribed circle: U[43.5; 16.27696153326]
Coordinates of the inscribed circle: I[32; 21.50328575161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.2932875183° = 137°17'34″ = 0.74553799421 rad
∠ B' = β' = 112.2010616997° = 112°12'2″ = 1.18333224642 rad
∠ C' = γ' = 110.5076507819° = 110°30'23″ = 1.21328902473 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 = 63 ; ; b = 86 ; ; c = 87 ; ;

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

p = a+b+c = 63+86+87 = 236 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 236 }{ 2 } = 118 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 118 * (118-63)(118-86)(118-87) } ; ; T = sqrt{ 6438080 } = 2537.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2537.34 }{ 63 } = 80.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2537.34 }{ 86 } = 59.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2537.34 }{ 87 } = 58.33 ; ;

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{ 63**2-86**2-87**2 }{ 2 * 86 * 87 } ) = 42° 42'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 86**2-63**2-87**2 }{ 2 * 63 * 87 } ) = 67° 47'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 87**2-63**2-86**2 }{ 2 * 86 * 63 } ) = 69° 29'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2537.34 }{ 118 } = 21.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 63 }{ 2 * sin 42° 42'26" } = 46.44 ; ;




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