Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 90   b = 90   c = 127.28

Area: T = 40509.9999997
Perimeter: p = 307.28
Semiperimeter: s = 153.64

Angle ∠ A = α = 454.9996491518° = 44°59'59″ = 0.78553920399 rad
Angle ∠ B = β = 454.9996491518° = 44°59'59″ = 0.78553920399 rad
Angle ∠ C = γ = 90.00107016965° = 90°3″ = 1.57108085737 rad

Height: ha = 909.9999999933
Height: hb = 909.9999999933
Height: hc = 63.63992206112

Median: ma = 100.6243551915
Median: mb = 100.6243551915
Median: mc = 63.63992206112

Inradius: r = 26.36603228306
Circumradius: R = 63.64400000048

Vertex coordinates: A[127.28; 0] B[0; 0] C[63.64; 63.63992206112]
Centroid: CG[63.64; 21.21330735371]
Coordinates of the circumscribed circle: U[63.64; -0.00107793936]
Coordinates of the inscribed circle: I[63.64; 26.36603228306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1355.000350848° = 135°1″ = 0.78553920399 rad
∠ B' = β' = 1355.000350848° = 135°1″ = 0.78553920399 rad
∠ C' = γ' = 89.99992983035° = 89°59'57″ = 1.57108085737 rad

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How did we calculate this triangle?

a = 90 ; ; b = 90 ; ; c = 127.28 ; ;

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

p = a+b+c = 90+90+127.28 = 307.28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 307.28 }{ 2 } = 153.64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 153.64 * (153.64-90)(153.64-90)(153.64-127.28) } ; ; T = sqrt{ 16402500 } = 4050 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4050 }{ 90 } = 90 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4050 }{ 90 } = 90 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4050 }{ 127.28 } = 63.64 ; ;

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{ 90**2+127.28**2-90**2 }{ 2 * 90 * 127.28 } ) = 44° 59'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 90**2+127.28**2-90**2 }{ 2 * 90 * 127.28 } ) = 44° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 44° 59'59" - 44° 59'59" = 90° 3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4050 }{ 153.64 } = 26.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 90 }{ 2 * sin 44° 59'59" } = 63.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 127.28**2 - 90**2 } }{ 2 } = 100.624 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 127.28**2+2 * 90**2 - 90**2 } }{ 2 } = 100.624 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 90**2 - 127.28**2 } }{ 2 } = 63.639 ; ;
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