4 23 26 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 23   c = 26

Area: T = 32.3022283201
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 6.20220192449° = 6°12'7″ = 0.10882456561 rad
Angle ∠ B = β = 38.40436536582° = 38°24'13″ = 0.67702702011 rad
Angle ∠ C = γ = 135.39443270969° = 135°23'40″ = 2.36330767964 rad

Height: ha = 16.15111416005
Height: hb = 2.80988941914
Height: hc = 2.48547910155

Median: ma = 24.46442596455
Median: mb = 14.62201915172
Median: mc = 10.17334949747

Inradius: r = 1.21989540831
Circumradius: R = 18.51326232805

Vertex coordinates: A[26; 0] B[0; 0] C[3.13546153846; 2.48547910155]
Centroid: CG[9.71215384615; 0.82882636718]
Coordinates of the circumscribed circle: U[13; -13.1880182879]
Coordinates of the inscribed circle: I[3.5; 1.21989540831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.79879807551° = 173°47'53″ = 0.10882456561 rad
∠ B' = β' = 141.59663463418° = 141°35'47″ = 0.67702702011 rad
∠ C' = γ' = 44.60656729031° = 44°36'20″ = 2.36330767964 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 = 4 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 4+23+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-4)(26.5-23)(26.5-26) } ; ; T = sqrt{ 1043.44 } = 32.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.3 }{ 4 } = 16.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.3 }{ 23 } = 2.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.3 }{ 26 } = 2.48 ; ;

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{ 23**2+26**2-4**2 }{ 2 * 23 * 26 } ) = 6° 12'7" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4**2+26**2-23**2 }{ 2 * 4 * 26 } ) = 38° 24'13" ; ; gamma = 180° - alpha - beta = 180° - 6° 12'7" - 38° 24'13" = 135° 23'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.3 }{ 26.5 } = 1.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 6° 12'7" } = 18.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 26**2 - 4**2 } }{ 2 } = 24.464 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 4**2 - 23**2 } }{ 2 } = 14.62 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 4**2 - 26**2 } }{ 2 } = 10.173 ; ;
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