Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 13.18   b = 13.18   c = 18.64

Area: T = 86.85661997787
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 44.99879550462° = 44°59'53″ = 0.78553624722 rad
Angle ∠ B = β = 44.99879550462° = 44°59'53″ = 0.78553624722 rad
Angle ∠ C = γ = 90.00440899076° = 90°15″ = 1.57108677091 rad

Height: ha = 13.18799999664
Height: hb = 13.18799999664
Height: hc = 9.31993347402

Median: ma = 14.7366108713
Median: mb = 14.7366108713
Median: mc = 9.31993347402

Inradius: r = 3.86602755457
Circumradius: R = 9.32200000237

Vertex coordinates: A[18.64; 0] B[0; 0] C[9.32; 9.31993347402]
Centroid: CG[9.32; 3.10664449134]
Coordinates of the circumscribed circle: U[9.32; -0.00106652835]
Coordinates of the inscribed circle: I[9.32; 3.86602755457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0022044954° = 135°7″ = 0.78553624722 rad
∠ B' = β' = 135.0022044954° = 135°7″ = 0.78553624722 rad
∠ C' = γ' = 89.99659100924° = 89°59'45″ = 1.57108677091 rad

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How did we calculate this triangle?

a = 13.18 ; ; b = 13.18 ; ; c = 18.64 ; ;

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

p = a+b+c = 13.18+13.18+18.64 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-13.18)(22.5-13.18)(22.5-18.64) } ; ; T = sqrt{ 7544 } = 86.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.86 }{ 13.18 } = 13.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.86 }{ 13.18 } = 13.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.86 }{ 18.64 } = 9.32 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 13.18**2+18.64**2-13.18**2 }{ 2 * 13.18 * 18.64 } ) = 44° 59'53" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.18**2+18.64**2-13.18**2 }{ 2 * 13.18 * 18.64 } ) = 44° 59'53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 13.18**2+13.18**2-18.64**2 }{ 2 * 13.18 * 13.18 } ) = 90° 15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.86 }{ 22.5 } = 3.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.18 }{ 2 * sin 44° 59'53" } = 9.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.18**2+2 * 18.64**2 - 13.18**2 } }{ 2 } = 14.736 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.64**2+2 * 13.18**2 - 13.18**2 } }{ 2 } = 14.736 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.18**2+2 * 13.18**2 - 18.64**2 } }{ 2 } = 9.319 ; ;
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