Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 78   b = 78   c = 65.93

Area: T = 2330.355010125
Perimeter: p = 221.93
Semiperimeter: s = 110.965

Angle ∠ A = α = 64.99993713884° = 64°59'58″ = 1.13444530425 rad
Angle ∠ B = β = 64.99993713884° = 64°59'58″ = 1.13444530425 rad
Angle ∠ C = γ = 50.00112572232° = 50°5″ = 0.87326865687 rad

Height: ha = 59.75325666988
Height: hb = 59.75325666988
Height: hc = 70.69216457228

Median: ma = 60.78114317864
Median: mb = 60.78114317864
Median: mc = 70.69216457228

Inradius: r = 21.00107669198
Circumradius: R = 43.03219589945

Vertex coordinates: A[65.93; 0] B[0; 0] C[32.965; 70.69216457228]
Centroid: CG[32.965; 23.56438819076]
Coordinates of the circumscribed circle: U[32.965; 27.66596867283]
Coordinates of the inscribed circle: I[32.965; 21.00107669198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.0010628612° = 115°2″ = 1.13444530425 rad
∠ B' = β' = 115.0010628612° = 115°2″ = 1.13444530425 rad
∠ C' = γ' = 129.9998742777° = 129°59'55″ = 0.87326865687 rad

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How did we calculate this triangle?

a = 78 ; ; b = 78 ; ; c = 65.93 ; ;

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

p = a+b+c = 78+78+65.93 = 221.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 221.93 }{ 2 } = 110.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 110.97 * (110.97-78)(110.97-78)(110.97-65.93) } ; ; T = sqrt{ 5430531.59 } = 2330.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2330.35 }{ 78 } = 59.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2330.35 }{ 78 } = 59.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2330.35 }{ 65.93 } = 70.69 ; ;

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{ 78**2+65.93**2-78**2 }{ 2 * 78 * 65.93 } ) = 64° 59'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 78**2+65.93**2-78**2 }{ 2 * 78 * 65.93 } ) = 64° 59'58" ; ; gamma = 180° - alpha - beta = 180° - 64° 59'58" - 64° 59'58" = 50° 5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2330.35 }{ 110.97 } = 21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 78 }{ 2 * sin 64° 59'58" } = 43.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 78**2+2 * 65.93**2 - 78**2 } }{ 2 } = 60.781 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 65.93**2+2 * 78**2 - 78**2 } }{ 2 } = 60.781 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 78**2+2 * 78**2 - 65.93**2 } }{ 2 } = 70.692 ; ;
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