Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 14   b = 20   c = 23

Area: T = 138.9944379383
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 37.18801691374° = 37°10'49″ = 0.64989163679 rad
Angle ∠ B = β = 59.69113221687° = 59°41'29″ = 1.04218101067 rad
Angle ∠ C = γ = 83.12985086939° = 83°7'43″ = 1.4510866179 rad

Height: ha = 19.85663399118
Height: hb = 13.89994379383
Height: hc = 12.08664677724

Median: ma = 20.38438171106
Median: mb = 16.2021851746
Median: mc = 12.87443931896

Inradius: r = 4.87769957678
Circumradius: R = 11.58332021924

Vertex coordinates: A[23; 0] B[0; 0] C[7.06552173913; 12.08664677724]
Centroid: CG[10.02217391304; 4.02988225908]
Coordinates of the circumscribed circle: U[11.5; 1.38658474052]
Coordinates of the inscribed circle: I[8.5; 4.87769957678]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.8219830863° = 142°49'11″ = 0.64989163679 rad
∠ B' = β' = 120.3098677831° = 120°18'31″ = 1.04218101067 rad
∠ C' = γ' = 96.87114913061° = 96°52'17″ = 1.4510866179 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 = 14+20+23 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-14)(28.5-20)(28.5-23) } ; ; T = sqrt{ 19319.44 } = 138.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 138.99 }{ 14 } = 19.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 138.99 }{ 20 } = 13.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 138.99 }{ 23 } = 12.09 ; ;

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{ 20**2+23**2-14**2 }{ 2 * 20 * 23 } ) = 37° 10'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+23**2-20**2 }{ 2 * 14 * 23 } ) = 59° 41'29" ; ; gamma = 180° - alpha - beta = 180° - 37° 10'49" - 59° 41'29" = 83° 7'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 138.99 }{ 28.5 } = 4.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 37° 10'49" } = 11.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 23**2 - 14**2 } }{ 2 } = 20.384 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 14**2 - 20**2 } }{ 2 } = 16.202 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 14**2 - 23**2 } }{ 2 } = 12.874 ; ;
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