Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 6   b = 21   c = 21

Area: T = 62.35438290725
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 16.42664214035° = 16°25'35″ = 0.28766951378 rad
Angle ∠ B = β = 81.78767892983° = 81°47'12″ = 1.42774487579 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 20.78546096908
Height: hb = 5.93884599117
Height: hc = 5.93884599117

Median: ma = 20.78546096908
Median: mb = 11.32547516529
Median: mc = 11.32547516529

Inradius: r = 2.59880762114
Circumradius: R = 10.60988111964

Vertex coordinates: A[21; 0] B[0; 0] C[0.85771428571; 5.93884599117]
Centroid: CG[7.28657142857; 1.97994866372]
Coordinates of the circumscribed circle: U[10.5; 1.51655444566]
Coordinates of the inscribed circle: I[3; 2.59880762114]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.5743578597° = 163°34'25″ = 0.28766951378 rad
∠ B' = β' = 98.21332107017° = 98°12'48″ = 1.42774487579 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 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 = 6+21+21 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-6)(24-21)(24-21) } ; ; T = sqrt{ 3888 } = 62.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.35 }{ 6 } = 20.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.35 }{ 21 } = 5.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.35 }{ 21 } = 5.94 ; ;

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{ 21**2+21**2-6**2 }{ 2 * 21 * 21 } ) = 16° 25'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+21**2-21**2 }{ 2 * 6 * 21 } ) = 81° 47'12" ; ; gamma = 180° - alpha - beta = 180° - 16° 25'35" - 81° 47'12" = 81° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.35 }{ 24 } = 2.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 16° 25'35" } = 10.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 21**2 - 6**2 } }{ 2 } = 20.785 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 6**2 - 21**2 } }{ 2 } = 11.325 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 6**2 - 21**2 } }{ 2 } = 11.325 ; ;
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