10 19 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 19   c = 26

Area: T = 78.33222251695
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 18.49897207034° = 18°29'23″ = 0.3232706504 rad
Angle ∠ B = β = 37.05331475504° = 37°3'11″ = 0.6476699423 rad
Angle ∠ C = γ = 124.4577131746° = 124°27'26″ = 2.17221867266 rad

Height: ha = 15.66664450339
Height: hb = 8.24554973863
Height: hc = 6.02655557823

Median: ma = 22.21548598915
Median: mb = 17.25554339267
Median: mc = 7.84221935707

Inradius: r = 2.84884445516
Circumradius: R = 15.76661804874

Vertex coordinates: A[26; 0] B[0; 0] C[7.98107692308; 6.02655557823]
Centroid: CG[11.32769230769; 2.00985185941]
Coordinates of the circumscribed circle: U[13; -8.922033896]
Coordinates of the inscribed circle: I[8.5; 2.84884445516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5110279297° = 161°30'37″ = 0.3232706504 rad
∠ B' = β' = 142.947685245° = 142°56'49″ = 0.6476699423 rad
∠ C' = γ' = 55.54328682537° = 55°32'34″ = 2.17221867266 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 10 ; ; b = 19 ; ; c = 26 ; ;

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

p = a+b+c = 10+19+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-10)(27.5-19)(27.5-26) } ; ; T = sqrt{ 6135.94 } = 78.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.33 }{ 10 } = 15.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.33 }{ 19 } = 8.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.33 }{ 26 } = 6.03 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 18° 29'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 37° 3'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-19**2 }{ 2 * 19 * 10 } ) = 124° 27'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.33 }{ 27.5 } = 2.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 29'23" } = 15.77 ; ;




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