Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 51   b = 110   c = 148.03

Area: T = 2148.79657948
Perimeter: p = 309.03
Semiperimeter: s = 154.515

Angle ∠ A = α = 15.30331648452° = 15°18'11″ = 0.26770906125 rad
Angle ∠ B = β = 34.69881422477° = 34°41'53″ = 0.60655968265 rad
Angle ∠ C = γ = 129.9998692907° = 129°59'55″ = 2.26989052145 rad

Height: ha = 84.2676501757
Height: hb = 39.0699014451
Height: hc = 29.0321896167

Median: ma = 127.891132281
Median: mb = 96.08329873078
Median: mc = 43.27698483358

Inradius: r = 13.90767132305
Circumradius: R = 96.6187871043

Vertex coordinates: A[148.03; 0] B[0; 0] C[41.93302874417; 29.0321896167]
Centroid: CG[63.32200958139; 9.67772987223]
Coordinates of the circumscribed circle: U[74.015; -62.10330818871]
Coordinates of the inscribed circle: I[44.515; 13.90767132305]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6976835155° = 164°41'49″ = 0.26770906125 rad
∠ B' = β' = 145.3021857752° = 145°18'7″ = 0.60655968265 rad
∠ C' = γ' = 50.00113070929° = 50°5″ = 2.26989052145 rad

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How did we calculate this triangle?

a = 51 ; ; b = 110 ; ; c = 148.03 ; ;

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

p = a+b+c = 51+110+148.03 = 309.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 309.03 }{ 2 } = 154.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 154.52 * (154.52-51)(154.52-110)(154.52-148.03) } ; ; T = sqrt{ 4617323.37 } = 2148.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2148.8 }{ 51 } = 84.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2148.8 }{ 110 } = 39.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2148.8 }{ 148.03 } = 29.03 ; ;

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{ 110**2+148.03**2-51**2 }{ 2 * 110 * 148.03 } ) = 15° 18'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 51**2+148.03**2-110**2 }{ 2 * 51 * 148.03 } ) = 34° 41'53" ; ; gamma = 180° - alpha - beta = 180° - 15° 18'11" - 34° 41'53" = 129° 59'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2148.8 }{ 154.52 } = 13.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 51 }{ 2 * sin 15° 18'11" } = 96.62 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 110**2+2 * 148.03**2 - 51**2 } }{ 2 } = 127.891 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 148.03**2+2 * 51**2 - 110**2 } }{ 2 } = 96.083 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 110**2+2 * 51**2 - 148.03**2 } }{ 2 } = 43.27 ; ;
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