Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 105.04   b = 105.04   c = 200.9

Area: T = 3084.975486486
Perimeter: p = 410.98
Semiperimeter: s = 205.49

Angle ∠ A = α = 177.0004693311° = 17°2″ = 0.29767141642 rad
Angle ∠ B = β = 177.0004693311° = 17°2″ = 0.29767141642 rad
Angle ∠ C = γ = 145.9999061338° = 145°59'57″ = 2.54881643252 rad

Height: ha = 58.73990492167
Height: hb = 58.73990492167
Height: hc = 30.71215466885

Median: ma = 151.4555456818
Median: mb = 151.4555456818
Median: mc = 30.71215466885

Inradius: r = 15.01327736866
Circumradius: R = 179.6329533346

Vertex coordinates: A[200.9; 0] B[0; 0] C[100.45; 30.71215466885]
Centroid: CG[100.45; 10.23771822295]
Coordinates of the circumscribed circle: U[100.45; -148.9187986658]
Coordinates of the inscribed circle: I[100.45; 15.01327736866]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1632.999530669° = 162°59'58″ = 0.29767141642 rad
∠ B' = β' = 1632.999530669° = 162°59'58″ = 0.29767141642 rad
∠ C' = γ' = 34.00109386622° = 34°3″ = 2.54881643252 rad

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How did we calculate this triangle?

a = 105.04 ; ; b = 105.04 ; ; c = 200.9 ; ;

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

p = a+b+c = 105.04+105.04+200.9 = 410.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 410.98 }{ 2 } = 205.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 205.49 * (205.49-105.04)(205.49-105.04)(205.49-200.9) } ; ; T = sqrt{ 9517069.92 } = 3084.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3084.97 }{ 105.04 } = 58.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3084.97 }{ 105.04 } = 58.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3084.97 }{ 200.9 } = 30.71 ; ;

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{ 105.04**2+200.9**2-105.04**2 }{ 2 * 105.04 * 200.9 } ) = 17° 2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 105.04**2+200.9**2-105.04**2 }{ 2 * 105.04 * 200.9 } ) = 17° 2" ; ; gamma = 180° - alpha - beta = 180° - 17° 2" - 17° 2" = 145° 59'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3084.97 }{ 205.49 } = 15.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 105.04 }{ 2 * sin 17° 2" } = 179.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.04**2+2 * 200.9**2 - 105.04**2 } }{ 2 } = 151.455 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 200.9**2+2 * 105.04**2 - 105.04**2 } }{ 2 } = 151.455 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.04**2+2 * 105.04**2 - 200.9**2 } }{ 2 } = 30.712 ; ;
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