Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 85   b = 90   c = 82.46

Area: T = 3176.165548155
Perimeter: p = 257.46
Semiperimeter: s = 128.73

Angle ∠ A = α = 58.86546013058° = 58°51'53″ = 1.02773811057 rad
Angle ∠ B = β = 64.99986277439° = 64°59'55″ = 1.13444400634 rad
Angle ∠ C = γ = 56.13767709503° = 56°8'12″ = 0.98797714845 rad

Height: ha = 74.73333054481
Height: hb = 70.58114551455
Height: hc = 77.0355301517

Median: ma = 75.1243736595
Median: mb = 70.62110011257
Median: mc = 77.21877900487

Inradius: r = 24.67330791699
Circumradius: R = 49.65325608997

Vertex coordinates: A[82.46; 0] B[0; 0] C[35.92443972835; 77.0355301517]
Centroid: CG[39.46114657612; 25.6788433839]
Coordinates of the circumscribed circle: U[41.23; 27.66770183413]
Coordinates of the inscribed circle: I[38.73; 24.67330791699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.1355398694° = 121°8'7″ = 1.02773811057 rad
∠ B' = β' = 115.0011372256° = 115°5″ = 1.13444400634 rad
∠ C' = γ' = 123.863322905° = 123°51'48″ = 0.98797714845 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 = 85+90+82.46 = 257.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 257.46 }{ 2 } = 128.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 128.73 * (128.73-85)(128.73-90)(128.73-82.46) } ; ; T = sqrt{ 10088027.17 } = 3176.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3176.17 }{ 85 } = 74.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3176.17 }{ 90 } = 70.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3176.17 }{ 82.46 } = 77.04 ; ;

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+82.46**2-85**2 }{ 2 * 90 * 82.46 } ) = 58° 51'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 85**2+82.46**2-90**2 }{ 2 * 85 * 82.46 } ) = 64° 59'55" ; ; gamma = 180° - alpha - beta = 180° - 58° 51'53" - 64° 59'55" = 56° 8'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3176.17 }{ 128.73 } = 24.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 85 }{ 2 * sin 58° 51'53" } = 49.65 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 82.46**2 - 85**2 } }{ 2 } = 75.124 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 82.46**2+2 * 85**2 - 90**2 } }{ 2 } = 70.621 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 85**2 - 82.46**2 } }{ 2 } = 77.218 ; ;
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