Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 18

Area: T = 71.43552853987
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 11.90658808998
Height: hb = 11.90658808998
Height: hc = 7.93772539332

Median: ma = 14.07112472795
Median: mb = 14.07112472795
Median: mc = 7.93772539332

Inradius: r = 3.40216802571
Circumradius: R = 9.07111473522

Vertex coordinates: A[18; 0] B[0; 0] C[9; 7.93772539332]
Centroid: CG[9; 2.64657513111]
Coordinates of the circumscribed circle: U[9; -1.1343893419]
Coordinates of the inscribed circle: I[9; 3.40216802571]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 rad

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How did we calculate this triangle?

a = 12 ; ; b = 12 ; ; c = 18 ; ;

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

p = a+b+c = 12+12+18 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-12)(21-12)(21-18) } ; ; T = sqrt{ 5103 } = 71.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.44 }{ 12 } = 11.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.44 }{ 12 } = 11.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.44 }{ 18 } = 7.94 ; ;

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{ 12**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 41° 24'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-12**2-18**2 }{ 2 * 12 * 18 } ) = 41° 24'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-12**2-12**2 }{ 2 * 12 * 12 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.44 }{ 21 } = 3.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 41° 24'35" } = 9.07 ; ;

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