Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 140   b = 140   c = 263.11

Area: T = 6299.93552769
Perimeter: p = 543.11
Semiperimeter: s = 271.555

Angle ∠ A = α = 20.00223534388° = 20°8″ = 0.34991069257 rad
Angle ∠ B = β = 20.00223534388° = 20°8″ = 0.34991069257 rad
Angle ∠ C = γ = 139.9955293122° = 139°59'43″ = 2.44333788023 rad

Height: ha = 89.99990753843
Height: hb = 89.99990753843
Height: hc = 47.88882237612

Median: ma = 198.7879868322
Median: mb = 198.7879868322
Median: mc = 47.88882237612

Inradius: r = 23.19994817879
Circumradius: R = 204.6433213515

Vertex coordinates: A[263.11; 0] B[0; 0] C[131.555; 47.88882237612]
Centroid: CG[131.555; 15.96327412537]
Coordinates of the circumscribed circle: U[131.555; -156.7554989754]
Coordinates of the inscribed circle: I[131.555; 23.19994817879]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.9987646561° = 159°59'52″ = 0.34991069257 rad
∠ B' = β' = 159.9987646561° = 159°59'52″ = 0.34991069257 rad
∠ C' = γ' = 40.00547068775° = 40°17″ = 2.44333788023 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 = 140+140+263.11 = 543.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 543.11 }{ 2 } = 271.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 271.56 * (271.56-140)(271.56-140)(271.56-263.11) } ; ; T = sqrt{ 39689184.49 } = 6299.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6299.94 }{ 140 } = 90 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6299.94 }{ 140 } = 90 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6299.94 }{ 263.11 } = 47.89 ; ;

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{ 140**2+263.11**2-140**2 }{ 2 * 140 * 263.11 } ) = 20° 8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 140**2+263.11**2-140**2 }{ 2 * 140 * 263.11 } ) = 20° 8" ; ; gamma = 180° - alpha - beta = 180° - 20° 8" - 20° 8" = 139° 59'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6299.94 }{ 271.56 } = 23.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 140 }{ 2 * sin 20° 8" } = 204.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 263.11**2 - 140**2 } }{ 2 } = 198.78 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 263.11**2+2 * 140**2 - 140**2 } }{ 2 } = 198.78 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 140**2 - 263.11**2 } }{ 2 } = 47.888 ; ;
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