Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 47   b = 16.07   c = 44.17

Area: T = 354.9065945187
Perimeter: p = 107.24
Semiperimeter: s = 53.62

Angle ∠ A = α = 89.9910563871° = 89°59'26″ = 1.57106316353 rad
Angle ∠ B = β = 19.99435824686° = 19°59'37″ = 0.34989538433 rad
Angle ∠ C = γ = 70.01658536604° = 70°57″ = 1.2222007175 rad

Height: ha = 15.10223806463
Height: hb = 44.1769999401
Height: hc = 16.07699997821

Median: ma = 23.50224871024
Median: mb = 44.89435766564
Median: mc = 27.31107163033

Inradius: r = 6.61989098319
Circumradius: R = 23.55000003187

Vertex coordinates: A[44.17; 0] B[0; 0] C[44.16773534073; 16.07699997821]
Centroid: CG[29.44657844691; 5.3576666594]
Coordinates of the circumscribed circle: U[22.085; 8.03113628967]
Coordinates of the inscribed circle: I[37.55; 6.61989098319]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.0099436129° = 90°34″ = 1.57106316353 rad
∠ B' = β' = 160.0066417531° = 160°23″ = 0.34989538433 rad
∠ C' = γ' = 109.984414634° = 109°59'3″ = 1.2222007175 rad

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How did we calculate this triangle?

a = 47 ; ; b = 16.07 ; ; c = 44.17 ; ;

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

p = a+b+c = 47+16.07+44.17 = 107.24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 107.24 }{ 2 } = 53.62 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.62 * (53.62-47)(53.62-16.07)(53.62-44.17) } ; ; T = sqrt{ 125958.23 } = 354.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 354.91 }{ 47 } = 15.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 354.91 }{ 16.07 } = 44.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 354.91 }{ 44.17 } = 16.07 ; ;

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{ 16.07**2+44.17**2-47**2 }{ 2 * 16.07 * 44.17 } ) = 89° 59'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 47**2+44.17**2-16.07**2 }{ 2 * 47 * 44.17 } ) = 19° 59'37" ; ; gamma = 180° - alpha - beta = 180° - 89° 59'26" - 19° 59'37" = 70° 57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 354.91 }{ 53.62 } = 6.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 47 }{ 2 * sin 89° 59'26" } = 23.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.07**2+2 * 44.17**2 - 47**2 } }{ 2 } = 23.502 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.17**2+2 * 47**2 - 16.07**2 } }{ 2 } = 44.894 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.07**2+2 * 47**2 - 44.17**2 } }{ 2 } = 27.311 ; ;
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