Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 42.43   b = 42.43   c = 60

Area: T = 900.1522437091
Perimeter: p = 144.86
Semiperimeter: s = 72.43

Angle ∠ A = α = 45.00548518124° = 45°17″ = 0.78554828435 rad
Angle ∠ B = β = 45.00548518124° = 45°17″ = 0.78554828435 rad
Angle ∠ C = γ = 89.99902963752° = 89°59'25″ = 1.57106269666 rad

Height: ha = 42.43299993915
Height: hb = 42.43299993915
Height: hc = 30.00550812364

Median: ma = 47.43549683778
Median: mb = 47.43549683778
Median: mc = 30.00550812364

Inradius: r = 12.42878950309
Circumradius: R = 300.0000004302

Vertex coordinates: A[60; 0] B[0; 0] C[30; 30.00550812364]
Centroid: CG[30; 10.00216937455]
Coordinates of the circumscribed circle: U[30; 0.00550808061]
Coordinates of the inscribed circle: I[30; 12.42878950309]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9955148188° = 134°59'43″ = 0.78554828435 rad
∠ B' = β' = 134.9955148188° = 134°59'43″ = 0.78554828435 rad
∠ C' = γ' = 90.01097036248° = 90°35″ = 1.57106269666 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 = 42.43+42.43+60 = 144.86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144.86 }{ 2 } = 72.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72.43 * (72.43-42.43)(72.43-42.43)(72.43-60) } ; ; T = sqrt{ 810274.41 } = 900.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 900.15 }{ 42.43 } = 42.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 900.15 }{ 42.43 } = 42.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 900.15 }{ 60 } = 30.01 ; ;

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{ 42.43**2+60**2-42.43**2 }{ 2 * 42.43 * 60 } ) = 45° 17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 42.43**2+60**2-42.43**2 }{ 2 * 42.43 * 60 } ) = 45° 17" ; ; gamma = 180° - alpha - beta = 180° - 45° 17" - 45° 17" = 89° 59'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 900.15 }{ 72.43 } = 12.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 42.43 }{ 2 * sin 45° 17" } = 30 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42.43**2+2 * 60**2 - 42.43**2 } }{ 2 } = 47.435 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 42.43**2 - 42.43**2 } }{ 2 } = 47.435 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42.43**2+2 * 42.43**2 - 60**2 } }{ 2 } = 30.005 ; ;
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