Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 5.321   b = 7.942   c = 9.707

Area: T = 21.1187780393
Perimeter: p = 22.97
Semiperimeter: s = 11.485

Angle ∠ A = α = 33.22197843724° = 33°13'11″ = 0.58797946141 rad
Angle ∠ B = β = 54.85663337337° = 54°51'23″ = 0.95774236392 rad
Angle ∠ C = γ = 91.92438818939° = 91°55'26″ = 1.60443744003 rad

Height: ha = 7.93875231697
Height: hb = 5.31880006026
Height: hc = 4.35110415974

Median: ma = 8.46600441045
Median: mb = 6.74554135529
Median: mc = 4.7055076009

Inradius: r = 1.83987270695
Circumradius: R = 4.85662374151

Vertex coordinates: A[9.707; 0] B[0; 0] C[3.06329198517; 4.35110415974]
Centroid: CG[4.25766399506; 1.45503471991]
Coordinates of the circumscribed circle: U[4.85435; -0.16330324565]
Coordinates of the inscribed circle: I[3.543; 1.83987270695]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7880215628° = 146°46'49″ = 0.58797946141 rad
∠ B' = β' = 125.1443666266° = 125°8'37″ = 0.95774236392 rad
∠ C' = γ' = 88.07661181061° = 88°4'34″ = 1.60443744003 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 5.321 ; ; b = 7.942 ; ; c = 9.707 ; ;

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

p = a+b+c = 5.32+7.94+9.71 = 22.97 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.97 }{ 2 } = 11.49 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.49 * (11.49-5.32)(11.49-7.94)(11.49-9.71) } ; ; T = sqrt{ 445.96 } = 21.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.12 }{ 5.32 } = 7.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.12 }{ 7.94 } = 5.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.12 }{ 9.71 } = 4.35 ; ;

6. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 7.94**2+9.71**2-5.32**2 }{ 2 * 7.94 * 9.71 } ) = 33° 13'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.32**2+9.71**2-7.94**2 }{ 2 * 5.32 * 9.71 } ) = 54° 51'23" ; ; gamma = 180° - alpha - beta = 180° - 33° 13'11" - 54° 51'23" = 91° 55'26" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.12 }{ 11.49 } = 1.84 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5.32 }{ 2 * sin 33° 13'11" } = 4.86 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.94**2+2 * 9.71**2 - 5.32**2 } }{ 2 } = 8.46 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.71**2+2 * 5.32**2 - 7.94**2 } }{ 2 } = 6.745 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.94**2+2 * 5.32**2 - 9.71**2 } }{ 2 } = 4.705 ; ;
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