Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 63.64   b = 63.64   c = 90

Area: T = 2025.025479985
Perimeter: p = 217.28
Semiperimeter: s = 108.64

Angle ∠ A = α = 455.0003508439° = 45°1″ = 0.78554042868 rad
Angle ∠ B = β = 455.0003508439° = 45°1″ = 0.78554042868 rad
Angle ∠ C = γ = 89.99992983121° = 89°59'57″ = 1.571078408 rad

Height: ha = 63.64399999952
Height: hb = 63.64399999952
Height: hc = 45.00105511077

Median: ma = 71.15113344921
Median: mb = 71.15113344921
Median: mc = 45.00105511077

Inradius: r = 18.64397717217
Circumradius: R = 455.0000000034

Vertex coordinates: A[90; 0] B[0; 0] C[45; 45.00105511077]
Centroid: CG[45; 155.0001837026]
Coordinates of the circumscribed circle: U[45; 0.00105511044]
Coordinates of the inscribed circle: I[45; 18.64397717217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1354.999649156° = 134°59'59″ = 0.78554042868 rad
∠ B' = β' = 1354.999649156° = 134°59'59″ = 0.78554042868 rad
∠ C' = γ' = 90.00107016879° = 90°3″ = 1.571078408 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 = 63.64+63.64+90 = 217.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 217.28 }{ 2 } = 108.64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 108.64 * (108.64-63.64)(108.64-63.64)(108.64-90) } ; ; T = sqrt{ 4100725.44 } = 2025.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2025.02 }{ 63.64 } = 63.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2025.02 }{ 63.64 } = 63.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2025.02 }{ 90 } = 45 ; ;

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{ 63.64**2+90**2-63.64**2 }{ 2 * 63.64 * 90 } ) = 45° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 63.64**2+90**2-63.64**2 }{ 2 * 63.64 * 90 } ) = 45° 1" ; ; gamma = 180° - alpha - beta = 180° - 45° 1" - 45° 1" = 89° 59'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2025.02 }{ 108.64 } = 18.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 63.64 }{ 2 * sin 45° 1" } = 45 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.64**2+2 * 90**2 - 63.64**2 } }{ 2 } = 71.151 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 63.64**2 - 63.64**2 } }{ 2 } = 71.151 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 63.64**2+2 * 63.64**2 - 90**2 } }{ 2 } = 45.001 ; ;
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