Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 7.81   b = 11.05   c = 7.81

Area: T = 30.49880375339
Perimeter: p = 26.67
Semiperimeter: s = 13.335

Angle ∠ A = α = 44.97440978303° = 44°58'27″ = 0.78549460853 rad
Angle ∠ B = β = 90.05218043395° = 90°3'6″ = 1.57217004831 rad
Angle ∠ C = γ = 44.97440978303° = 44°58'27″ = 0.78549460853 rad

Height: ha = 7.81099968077
Height: hb = 5.52200067935
Height: hc = 7.81099968077

Median: ma = 8.7355002862
Median: mb = 5.52200067935
Median: mc = 8.7355002862

Inradius: r = 2.28770669317
Circumradius: R = 5.52550022583

Vertex coordinates: A[7.81; 0] B[0; 0] C[-0.00770614597; 7.81099968077]
Centroid: CG[2.60109795134; 2.60333322692]
Coordinates of the circumscribed circle: U[3.905; 3.90985323274]
Coordinates of the inscribed circle: I[2.285; 2.28770669317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.026590217° = 135°1'33″ = 0.78549460853 rad
∠ B' = β' = 89.94881956605° = 89°56'54″ = 1.57217004831 rad
∠ C' = γ' = 135.026590217° = 135°1'33″ = 0.78549460853 rad

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How did we calculate this triangle?

a = 7.81 ; ; b = 11.05 ; ; c = 7.81 ; ;

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

p = a+b+c = 7.81+11.05+7.81 = 26.67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.67 }{ 2 } = 13.34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.34 * (13.34-7.81)(13.34-11.05)(13.34-7.81) } ; ; T = sqrt{ 930.13 } = 30.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.5 }{ 7.81 } = 7.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.5 }{ 11.05 } = 5.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.5 }{ 7.81 } = 7.81 ; ;

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{ 11.05**2+7.81**2-7.81**2 }{ 2 * 11.05 * 7.81 } ) = 44° 58'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.81**2+7.81**2-11.05**2 }{ 2 * 7.81 * 7.81 } ) = 90° 3'6" ; ; gamma = 180° - alpha - beta = 180° - 44° 58'27" - 90° 3'6" = 44° 58'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.5 }{ 13.34 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.81 }{ 2 * sin 44° 58'27" } = 5.53 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.05**2+2 * 7.81**2 - 7.81**2 } }{ 2 } = 8.735 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.81**2+2 * 7.81**2 - 11.05**2 } }{ 2 } = 5.52 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.05**2+2 * 7.81**2 - 7.81**2 } }{ 2 } = 8.735 ; ;
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