Triangle calculator

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

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 4.7   b = 4.7   c = 8.47

Area: T = 8.632231281
Perimeter: p = 17.87
Semiperimeter: s = 8.935

Angle ∠ A = α = 25.70217428331° = 25°42'6″ = 0.44985800359 rad
Angle ∠ B = β = 25.70217428331° = 25°42'6″ = 0.44985800359 rad
Angle ∠ C = γ = 128.5976514334° = 128°35'47″ = 2.24444325817 rad

Height: ha = 3.67333246
Height: hb = 3.67333246
Height: hc = 2.03883265195

Median: ma = 6.4343735307
Median: mb = 6.4343735307
Median: mc = 2.03883265195

Inradius: r = 0.96661234259
Circumradius: R = 5.41986607957

Vertex coordinates: A[8.47; 0] B[0; 0] C[4.235; 2.03883265195]
Centroid: CG[4.235; 0.67994421732]
Coordinates of the circumscribed circle: U[4.235; -3.38803342763]
Coordinates of the inscribed circle: I[4.235; 0.96661234259]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.2988257167° = 154°17'54″ = 0.44985800359 rad
∠ B' = β' = 154.2988257167° = 154°17'54″ = 0.44985800359 rad
∠ C' = γ' = 51.40334856661° = 51°24'13″ = 2.24444325817 rad

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How did we calculate this triangle?

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

a = 4.7 ; ; b = 4.7 ; ; c = 8.47 ; ;

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

p = a+b+c = 4.7+4.7+8.47 = 17.87 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.87 }{ 2 } = 8.94 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.94 * (8.94-4.7)(8.94-4.7)(8.94-8.47) } ; ; T = sqrt{ 74.52 } = 8.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.63 }{ 4.7 } = 3.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.63 }{ 4.7 } = 3.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.63 }{ 8.47 } = 2.04 ; ;

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{ 4.7**2+8.47**2-4.7**2 }{ 2 * 4.7 * 8.47 } ) = 25° 42'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.7**2+8.47**2-4.7**2 }{ 2 * 4.7 * 8.47 } ) = 25° 42'6" ; ;
 gamma = 180° - alpha - beta = 180° - 25° 42'6" - 25° 42'6" = 128° 35'47" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.63 }{ 8.94 } = 0.97 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.7 }{ 2 * sin 25° 42'6" } = 5.42 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.7**2+2 * 8.47**2 - 4.7**2 } }{ 2 } = 6.434 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.47**2+2 * 4.7**2 - 4.7**2 } }{ 2 } = 6.434 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.7**2+2 * 4.7**2 - 8.47**2 } }{ 2 } = 2.038 ; ;
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