Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 3   b = 6   c = 6

Area: T = 8.7144212529
Perimeter: p = 15
Semiperimeter: s = 7.5

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 = 5.80994750193
Height: hb = 2.90547375097
Height: hc = 2.90547375097

Median: ma = 5.80994750193
Median: mb = 3.67442346142
Median: mc = 3.67442346142

Inradius: r = 1.16218950039
Circumradius: R = 3.0988386677

Vertex coordinates: A[6; 0] B[0; 0] C[0.75; 2.90547375097]
Centroid: CG[2.25; 0.96882458366]
Coordinates of the circumscribed circle: U[3; 0.77545966692]
Coordinates of the inscribed circle: I[1.5; 1.16218950039]

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?

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

p = a+b+c = 3+6+6 = 15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15 }{ 2 } = 7.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.5 * (7.5-3)(7.5-6)(7.5-6) } ; ; T = sqrt{ 75.94 } = 8.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.71 }{ 3 } = 5.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.71 }{ 6 } = 2.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.71 }{ 6 } = 2.9 ; ;

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{ 6**2+6**2-3**2 }{ 2 * 6 * 6 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3**2+6**2-6**2 }{ 2 * 3 * 6 } ) = 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{ 8.71 }{ 7.5 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3 }{ 2 * sin 28° 57'18" } = 3.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6**2 - 3**2 } }{ 2 } = 5.809 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 3**2 - 6**2 } }{ 2 } = 3.674 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 3**2 - 6**2 } }{ 2 } = 3.674 ; ;
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