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 = 135.3944327097° = 135°23'40″ = 2.36330767964 rad

Height: h_a = 16.15111416005
Height: h_b = 2.80988941914
Height: h_c = 2.48547910155

Median: m_a = 24.46442596455
Median: m_b = 14.62201915172
Median: m_c = 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' = 173.7987980755° = 173°47'53″ = 0.10882456561 rad
∠ B' = β' = 141.5966346342° = 141°35'47″ = 0.67702702011 rad
∠ C' = γ' = 44.60656729031° = 44°36'20″ = 2.36330767964 rad

Calculate another triangle

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

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

6. Inradius

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

7. Circumradius

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

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