110 90 176.76 triangle

Obtuse scalene triangle.

Sides: a = 110   b = 90   c = 176.76

Area: T = 4108.4365744
Perimeter: p = 376.76
Semiperimeter: s = 188.38

Angle ∠ A = α = 31.09985391201° = 31°5'55″ = 0.54327719002 rad
Angle ∠ B = β = 24.99988654427° = 24°59'56″ = 0.43663125112 rad
Angle ∠ C = γ = 123.9032595437° = 123°54'9″ = 2.16325082421 rad

Height: ha = 74.69988317092
Height: hb = 91.2998572089
Height: hc = 46.48660346685

Median: ma = 129.0233442831
Median: mb = 140.1687930712
Median: mc = 47.84332398568

Inradius: r = 21.80992989914
Circumradius: R = 106.484359309

Vertex coordinates: A[176.76; 0] B[0; 0] C[99.69547770989; 46.48660346685]
Centroid: CG[92.15215923663; 15.49553448895]
Coordinates of the circumscribed circle: U[88.38; -59.39547068122]
Coordinates of the inscribed circle: I[98.38; 21.80992989914]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.901146088° = 148°54'5″ = 0.54327719002 rad
∠ B' = β' = 155.0011134557° = 155°4″ = 0.43663125112 rad
∠ C' = γ' = 56.09774045628° = 56°5'51″ = 2.16325082421 rad

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How did we calculate this triangle?

a = 110 ; ; b = 90 ; ; c = 176.76 ; ;

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

p = a+b+c = 110+90+176.76 = 376.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 376.76 }{ 2 } = 188.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 188.38 * (188.38-110)(188.38-90)(188.38-176.76) } ; ; T = sqrt{ 16879244.26 } = 4108.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4108.44 }{ 110 } = 74.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4108.44 }{ 90 } = 91.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4108.44 }{ 176.76 } = 46.49 ; ;

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{ 90**2+176.76**2-110**2 }{ 2 * 90 * 176.76 } ) = 31° 5'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 110**2+176.76**2-90**2 }{ 2 * 110 * 176.76 } ) = 24° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 31° 5'55" - 24° 59'56" = 123° 54'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4108.44 }{ 188.38 } = 21.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 110 }{ 2 * sin 31° 5'55" } = 106.48 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 176.76**2 - 110**2 } }{ 2 } = 129.023 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 176.76**2+2 * 110**2 - 90**2 } }{ 2 } = 140.168 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 110**2 - 176.76**2 } }{ 2 } = 47.843 ; ;
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