Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 30.02   b = 30.02   c = 42.45

Area: T = 450.6600188998
Perimeter: p = 102.49
Semiperimeter: s = 51.245

Angle ∠ A = α = 45.00663306977° = 45°23″ = 0.78655086549 rad
Angle ∠ B = β = 45.00663306977° = 45°23″ = 0.78655086549 rad
Angle ∠ C = γ = 89.98773386046° = 89°59'14″ = 1.57105753438 rad

Height: ha = 30.0219999267
Height: hb = 30.0219999267
Height: hc = 21.23296908833

Median: ma = 33.56604134361
Median: mb = 33.56604134361
Median: mc = 21.23296908833

Inradius: r = 8.79330566689
Circumradius: R = 21.22550005182

Vertex coordinates: A[42.45; 0] B[0; 0] C[21.225; 21.23296908833]
Centroid: CG[21.225; 7.07765636278]
Coordinates of the circumscribed circle: U[21.225; 0.0054690365]
Coordinates of the inscribed circle: I[21.225; 8.79330566689]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9943669302° = 134°59'37″ = 0.78655086549 rad
∠ B' = β' = 134.9943669302° = 134°59'37″ = 0.78655086549 rad
∠ C' = γ' = 90.01326613954° = 90°46″ = 1.57105753438 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 = 30.02+30.02+42.45 = 102.49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 102.49 }{ 2 } = 51.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 51.25 * (51.25-30.02)(51.25-30.02)(51.25-42.45) } ; ; T = sqrt{ 203040.53 } = 450.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 450.6 }{ 30.02 } = 30.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 450.6 }{ 30.02 } = 30.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 450.6 }{ 42.45 } = 21.23 ; ;

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{ 30.02**2+42.45**2-30.02**2 }{ 2 * 30.02 * 42.45 } ) = 45° 23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 30.02**2+42.45**2-30.02**2 }{ 2 * 30.02 * 42.45 } ) = 45° 23" ; ; gamma = 180° - alpha - beta = 180° - 45° 23" - 45° 23" = 89° 59'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 450.6 }{ 51.25 } = 8.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 30.02 }{ 2 * sin 45° 23" } = 21.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.02**2+2 * 42.45**2 - 30.02**2 } }{ 2 } = 33.56 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 42.45**2+2 * 30.02**2 - 30.02**2 } }{ 2 } = 33.56 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.02**2+2 * 30.02**2 - 42.45**2 } }{ 2 } = 21.23 ; ;
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