Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 12   b = 24   c = 24

Area: T = 139.4277400463
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 23.23879000772
Height: hb = 11.61989500386
Height: hc = 11.61989500386

Median: ma = 23.23879000772
Median: mb = 14.69769384567
Median: mc = 14.69769384567

Inradius: r = 4.64875800154
Circumradius: R = 12.39435467079

Vertex coordinates: A[24; 0] B[0; 0] C[3; 11.61989500386]
Centroid: CG[9; 3.87329833462]
Coordinates of the circumscribed circle: U[12; 3.0988386677]
Coordinates of the inscribed circle: I[6; 4.64875800154]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad

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How did we calculate this triangle?

a = 12 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 12+24+24 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-12)(30-24)(30-24) } ; ; T = sqrt{ 19440 } = 139.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 139.43 }{ 12 } = 23.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 139.43 }{ 24 } = 11.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 139.43 }{ 24 } = 11.62 ; ;

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{ 24**2+24**2-12**2 }{ 2 * 24 * 24 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12**2+24**2-24**2 }{ 2 * 12 * 24 } ) = 75° 31'21" ; ; gamma = 180° - alpha - beta = 180° - 28° 57'18" - 75° 31'21" = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 139.43 }{ 30 } = 4.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 28° 57'18" } = 12.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 12**2 } }{ 2 } = 23.238 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 12**2 - 24**2 } }{ 2 } = 14.697 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 12**2 - 24**2 } }{ 2 } = 14.697 ; ;
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