100 100 141.42 triangle

Acute isosceles triangle.

Sides: a = 100   b = 100   c = 141.42

Area: T = 50009.99999908
Perimeter: p = 341.42
Semiperimeter: s = 170.71

Angle ∠ A = α = 45.00105494665° = 45°2″ = 0.78554077534 rad
Angle ∠ B = β = 45.00105494665° = 45°2″ = 0.78554077534 rad
Angle ∠ C = γ = 89.99989010669° = 89°59'56″ = 1.57107771468 rad

Height: ha = 100.9999999816
Height: hb = 100.9999999816
Height: hc = 70.71113562308

Median: ma = 111.8032541116
Median: mb = 111.8032541116
Median: mc = 70.71113562308

Inradius: r = 29.28994382232
Circumradius: R = 70.7110000013

Vertex coordinates: A[141.42; 0] B[0; 0] C[70.71; 70.71113562308]
Centroid: CG[70.71; 23.57704520769]
Coordinates of the circumscribed circle: U[70.71; 0.00113562178]
Coordinates of the inscribed circle: I[70.71; 29.28994382232]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9999450533° = 134°59'58″ = 0.78554077534 rad
∠ B' = β' = 134.9999450533° = 134°59'58″ = 0.78554077534 rad
∠ C' = γ' = 90.00110989331° = 90°4″ = 1.57107771468 rad

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How did we calculate this triangle?

a = 100 ; ; b = 100 ; ; c = 141.42 ; ;

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

p = a+b+c = 100+100+141.42 = 341.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 341.42 }{ 2 } = 170.71 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 170.71 * (170.71-100)(170.71-100)(170.71-141.42) } ; ; T = sqrt{ 24999999.99 } = 5000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5000 }{ 100 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5000 }{ 100 } = 100 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5000 }{ 141.42 } = 70.71 ; ;

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{ 100**2+141.42**2-100**2 }{ 2 * 100 * 141.42 } ) = 45° 2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+141.42**2-100**2 }{ 2 * 100 * 141.42 } ) = 45° 2" ; ; gamma = 180° - alpha - beta = 180° - 45° 2" - 45° 2" = 89° 59'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5000 }{ 170.71 } = 29.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 45° 2" } = 70.71 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 141.42**2 - 100**2 } }{ 2 } = 111.803 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 141.42**2+2 * 100**2 - 100**2 } }{ 2 } = 111.803 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 100**2 - 141.42**2 } }{ 2 } = 70.711 ; ;
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