Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 21   b = 28   c = 28

Area: T = 272.5455294401
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 44.04986256741° = 44°2'55″ = 0.7698793549 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 67.9765687163° = 67°58'32″ = 1.18663995523 rad

Height: ha = 25.95766947048
Height: hb = 19.46875210286
Height: hc = 19.46875210286

Median: ma = 25.95766947048
Median: mb = 20.4088331632
Median: mc = 20.4088331632

Inradius: r = 7.07990985559
Circumradius: R = 15.10220769192

Vertex coordinates: A[28; 0] B[0; 0] C[7.875; 19.46875210286]
Centroid: CG[11.95883333333; 6.48991736762]
Coordinates of the circumscribed circle: U[14; 5.66332788447]
Coordinates of the inscribed circle: I[10.5; 7.07990985559]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9511374326° = 135°57'5″ = 0.7698793549 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad

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How did we calculate this triangle?

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

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

p = a+b+c = 21+28+28 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-21)(38.5-28)(38.5-28) } ; ; T = sqrt{ 74280.94 } = 272.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 272.55 }{ 21 } = 25.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 272.55 }{ 28 } = 19.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 272.55 }{ 28 } = 19.47 ; ;

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{ 28**2+28**2-21**2 }{ 2 * 28 * 28 } ) = 44° 2'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 21**2+28**2-28**2 }{ 2 * 21 * 28 } ) = 67° 58'32" ; ; gamma = 180° - alpha - beta = 180° - 44° 2'55" - 67° 58'32" = 67° 58'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 272.55 }{ 38.5 } = 7.08 ; ;

7. Circumradius

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

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 21**2 } }{ 2 } = 25.957 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 21**2 - 28**2 } }{ 2 } = 20.408 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 21**2 - 28**2 } }{ 2 } = 20.408 ; ;
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