48.375 126.75 149 triangle

Obtuse scalene triangle.

Sides: a = 48.375   b = 126.75   c = 149

Area: T = 2915.245466715
Perimeter: p = 324.125
Semiperimeter: s = 162.06325

Angle ∠ A = α = 17.98223657398° = 17°58'57″ = 0.31438514895 rad
Angle ∠ B = β = 53.98991278753° = 53°59'21″ = 0.94222880417 rad
Angle ∠ C = γ = 108.0298506385° = 108°1'43″ = 1.88554531224 rad

Height: ha = 120.5276911303
Height: hb = 465.9999158525
Height: hc = 39.13108009013

Median: ma = 136.1921945774
Median: mb = 90.85325161319
Median: mc = 60.43767567172

Inradius: r = 17.98883974834
Circumradius: R = 78.34766107103

Vertex coordinates: A[149; 0] B[0; 0] C[28.44215373322; 39.13108009013]
Centroid: CG[59.14771791107; 13.04436003004]
Coordinates of the circumscribed circle: U[74.5; -24.24875031662]
Coordinates of the inscribed circle: I[35.31325; 17.98883974834]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.018763426° = 162°1'3″ = 0.31438514895 rad
∠ B' = β' = 126.0110872125° = 126°39″ = 0.94222880417 rad
∠ C' = γ' = 71.97114936151° = 71°58'17″ = 1.88554531224 rad

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How did we calculate this triangle?

a = 48.38 ; ; b = 126.75 ; ; c = 149 ; ;

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

p = a+b+c = 48.38+126.75+149 = 324.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 324.13 }{ 2 } = 162.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 162.06 * (162.06-48.38)(162.06-126.75)(162.06-149) } ; ; T = sqrt{ 8498651.47 } = 2915.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2915.24 }{ 48.38 } = 120.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2915.24 }{ 126.75 } = 46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2915.24 }{ 149 } = 39.13 ; ;

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{ 48.38**2-126.75**2-149**2 }{ 2 * 126.75 * 149 } ) = 17° 58'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 126.75**2-48.38**2-149**2 }{ 2 * 48.38 * 149 } ) = 53° 59'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 149**2-48.38**2-126.75**2 }{ 2 * 126.75 * 48.38 } ) = 108° 1'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2915.24 }{ 162.06 } = 17.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48.38 }{ 2 * sin 17° 58'57" } = 78.35 ; ;




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