Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12.35   b = 8.75   c = 14.48

Area: T = 53.81328057087
Perimeter: p = 35.58
Semiperimeter: s = 17.79

Angle ∠ A = α = 58.15221526879° = 58°9'8″ = 1.01549465315 rad
Angle ∠ B = β = 37.00216987954° = 37°6″ = 0.64658014728 rad
Angle ∠ C = γ = 84.84661485167° = 84°50'46″ = 1.48108446493 rad

Height: ha = 8.71546244063
Height: hb = 12.33000698763
Height: hc = 7.43327079708

Median: ma = 10.24662590734
Median: mb = 12.72661865851
Median: mc = 7.88219350416

Inradius: r = 3.02548907088
Circumradius: R = 7.26993895969

Vertex coordinates: A[14.48; 0] B[0; 0] C[9.86329281768; 7.43327079708]
Centroid: CG[8.11443093923; 2.47875693236]
Coordinates of the circumscribed circle: U[7.24; 0.65330123367]
Coordinates of the inscribed circle: I[9.04; 3.02548907088]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.8487847312° = 121°50'52″ = 1.01549465315 rad
∠ B' = β' = 142.9988301205° = 142°59'54″ = 0.64658014728 rad
∠ C' = γ' = 95.15438514833° = 95°9'14″ = 1.48108446493 rad

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How did we calculate this triangle?

a = 12.35 ; ; b = 8.75 ; ; c = 14.48 ; ;

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

p = a+b+c = 12.35+8.75+14.48 = 35.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.58 }{ 2 } = 17.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.79 * (17.79-12.35)(17.79-8.75)(17.79-14.48) } ; ; T = sqrt{ 2895.82 } = 53.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.81 }{ 12.35 } = 8.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.81 }{ 8.75 } = 12.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.81 }{ 14.48 } = 7.43 ; ;

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{ 8.75**2+14.48**2-12.35**2 }{ 2 * 8.75 * 14.48 } ) = 58° 9'8" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.35**2+14.48**2-8.75**2 }{ 2 * 12.35 * 14.48 } ) = 37° 6" ; ; gamma = 180° - alpha - beta = 180° - 58° 9'8" - 37° 6" = 84° 50'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.81 }{ 17.79 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.35 }{ 2 * sin 58° 9'8" } = 7.27 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.75**2+2 * 14.48**2 - 12.35**2 } }{ 2 } = 10.246 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.48**2+2 * 12.35**2 - 8.75**2 } }{ 2 } = 12.726 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.75**2+2 * 12.35**2 - 14.48**2 } }{ 2 } = 7.882 ; ;
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