Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 21   b = 26   c = 28

Area: T = 259.9976995175
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 45.5844015584° = 45°35'2″ = 0.79655911582 rad
Angle ∠ B = β = 62.1710842728° = 62°10'15″ = 1.08550859043 rad
Angle ∠ C = γ = 72.24551416879° = 72°14'43″ = 1.2610915591 rad

Height: ha = 24.76216185881
Height: hb = 209.9997688596
Height: hc = 18.57112139411

Median: ma = 24.8954778569
Median: mb = 21.05994396887
Median: mc = 19.03994327647

Inradius: r = 6.93332532047
Circumradius: R = 14.77001698901

Vertex coordinates: A[28; 0] B[0; 0] C[9.80435714286; 18.57112139411]
Centroid: CG[12.60111904762; 6.1990404647]
Coordinates of the circumscribed circle: U[14; 4.48327441149]
Coordinates of the inscribed circle: I[11.5; 6.93332532047]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4165984416° = 134°24'58″ = 0.79655911582 rad
∠ B' = β' = 117.8299157272° = 117°49'45″ = 1.08550859043 rad
∠ C' = γ' = 107.7554858312° = 107°45'17″ = 1.2610915591 rad

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How did we calculate this triangle?

a = 21 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 21+26+28 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-21)(37.5-26)(37.5-28) } ; ; T = sqrt{ 67598.44 } = 260 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 260 }{ 21 } = 24.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 260 }{ 26 } = 20 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 260 }{ 28 } = 18.57 ; ;

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{ 26**2+28**2-21**2 }{ 2 * 26 * 28 } ) = 45° 35'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 21**2+28**2-26**2 }{ 2 * 21 * 28 } ) = 62° 10'15" ; ; gamma = 180° - alpha - beta = 180° - 45° 35'2" - 62° 10'15" = 72° 14'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 260 }{ 37.5 } = 6.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 21 }{ 2 * sin 45° 35'2" } = 14.7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 28**2 - 21**2 } }{ 2 } = 24.895 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 21**2 - 26**2 } }{ 2 } = 21.059 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 21**2 - 28**2 } }{ 2 } = 19.039 ; ;
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