10.77 7.07 14.21 triangle

Obtuse scalene triangle.

Sides: a = 10.77   b = 7.07   c = 14.21

Area: T = 36.99661463746
Perimeter: p = 32.05
Semiperimeter: s = 16.025

Angle ∠ A = α = 47.43441513042° = 47°26'3″ = 0.82878821181 rad
Angle ∠ B = β = 28.91328021753° = 28°54'46″ = 0.50546235939 rad
Angle ∠ C = γ = 103.653304652° = 103°39'11″ = 1.80990869415 rad

Height: ha = 6.8770222168
Height: hb = 10.46656708273
Height: hc = 5.20770578993

Median: ma = 9.8476637751
Median: mb = 12.10221599312
Median: mc = 5.70215677669

Inradius: r = 2.30986518799
Circumradius: R = 7.31216048902

Vertex coordinates: A[14.21; 0] B[0; 0] C[9.42875897255; 5.20770578993]
Centroid: CG[7.87991965752; 1.73656859664]
Coordinates of the circumscribed circle: U[7.105; -1.72658450307]
Coordinates of the inscribed circle: I[8.955; 2.30986518799]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.5665848696° = 132°33'57″ = 0.82878821181 rad
∠ B' = β' = 151.0877197825° = 151°5'14″ = 0.50546235939 rad
∠ C' = γ' = 76.34769534795° = 76°20'49″ = 1.80990869415 rad

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How did we calculate this triangle?

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

p = a+b+c = 10.77+7.07+14.21 = 32.05 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.05 }{ 2 } = 16.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.03 * (16.03-10.77)(16.03-7.07)(16.03-14.21) } ; ; T = sqrt{ 1368.71 } = 37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 37 }{ 10.77 } = 6.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 37 }{ 7.07 } = 10.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 37 }{ 14.21 } = 5.21 ; ;

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{ 7.07**2+14.21**2-10.77**2 }{ 2 * 7.07 * 14.21 } ) = 47° 26'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.77**2+14.21**2-7.07**2 }{ 2 * 10.77 * 14.21 } ) = 28° 54'46" ; ;
 gamma = 180° - alpha - beta = 180° - 47° 26'3" - 28° 54'46" = 103° 39'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 37 }{ 16.03 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.77 }{ 2 * sin 47° 26'3" } = 7.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 14.21**2 - 10.77**2 } }{ 2 } = 9.847 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.21**2+2 * 10.77**2 - 7.07**2 } }{ 2 } = 12.102 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 10.77**2 - 14.21**2 } }{ 2 } = 5.702 ; ;
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