Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 21   b = 24   c = 30

Area: T = 250.297669894
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ C = γ = 83.33545727438° = 83°20'4″ = 1.45444626751 rad

Height: ha = 23.83877808514
Height: hb = 20.8588058245
Height: hc = 16.6866446596

Median: ma = 25.05549396327
Median: mb = 22.94655878112
Median: mc = 16.83774582405

Inradius: r = 6.67545786384
Circumradius: R = 15.10220769192

Vertex coordinates: A[30; 0] B[0; 0] C[12.75; 16.6866446596]
Centroid: CG[14.25; 5.56221488653]
Coordinates of the circumscribed circle: U[15; 1.75329196424]
Coordinates of the inscribed circle: I[13.5; 6.67545786384]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ C' = γ' = 96.66554272562° = 96°39'56″ = 1.45444626751 rad

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How did we calculate this triangle?

a = 21 ; ; b = 24 ; ; c = 30 ; ;

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

p = a+b+c = 21+24+30 = 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)(37.5-24)(37.5-30) } ; ; T = sqrt{ 62648.44 } = 250.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 250.3 }{ 21 } = 23.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 250.3 }{ 24 } = 20.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 250.3 }{ 30 } = 16.69 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 21**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 44° 2'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-21**2-30**2 }{ 2 * 21 * 30 } ) = 52° 37' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-21**2-24**2 }{ 2 * 24 * 21 } ) = 83° 20'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 250.3 }{ 37.5 } = 6.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 21 }{ 2 * sin 44° 2'55" } = 15.1 ; ;

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