Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 51.08   b = 51.08   c = 96

Area: T = 838.5132603125
Perimeter: p = 198.16
Semiperimeter: s = 99.08

Angle ∠ A = α = 19.99883570875° = 19°59'54″ = 0.34990371762 rad
Angle ∠ B = β = 19.99883570875° = 19°59'54″ = 0.34990371762 rad
Angle ∠ C = γ = 140.0033285825° = 140°12″ = 2.44435183013 rad

Height: ha = 32.83113470292
Height: hb = 32.83113470292
Height: hc = 17.46990125651

Median: ma = 72.52878677475
Median: mb = 72.52878677475
Median: mc = 17.46990125651

Inradius: r = 8.46329854978
Circumradius: R = 74.68798478241

Vertex coordinates: A[96; 0] B[0; 0] C[48; 17.46990125651]
Centroid: CG[48; 5.82330041884]
Coordinates of the circumscribed circle: U[48; -57.2110835259]
Coordinates of the inscribed circle: I[48; 8.46329854978]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.0021642912° = 160°6″ = 0.34990371762 rad
∠ B' = β' = 160.0021642912° = 160°6″ = 0.34990371762 rad
∠ C' = γ' = 39.9976714175° = 39°59'48″ = 2.44435183013 rad

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How did we calculate this triangle?

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

p = a+b+c = 51.08+51.08+96 = 198.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 198.16 }{ 2 } = 99.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 99.08 * (99.08-51.08)(99.08-51.08)(99.08-96) } ; ; T = sqrt{ 703103.39 } = 838.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 838.51 }{ 51.08 } = 32.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 838.51 }{ 51.08 } = 32.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 838.51 }{ 96 } = 17.47 ; ;

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{ 51.08**2+96**2-51.08**2 }{ 2 * 51.08 * 96 } ) = 19° 59'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 51.08**2+96**2-51.08**2 }{ 2 * 51.08 * 96 } ) = 19° 59'54" ; ; gamma = 180° - alpha - beta = 180° - 19° 59'54" - 19° 59'54" = 140° 12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 838.51 }{ 99.08 } = 8.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 51.08 }{ 2 * sin 19° 59'54" } = 74.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 51.08**2+2 * 96**2 - 51.08**2 } }{ 2 } = 72.528 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 96**2+2 * 51.08**2 - 51.08**2 } }{ 2 } = 72.528 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 51.08**2+2 * 51.08**2 - 96**2 } }{ 2 } = 17.469 ; ;
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