31 35 39 triangle

Acute scalene triangle.

Sides: a = 31   b = 35   c = 39

Area: T = 516.3988283789
Perimeter: p = 105
Semiperimeter: s = 52.5

Angle ∠ A = α = 49.16877829725° = 49°10'4″ = 0.85881396988 rad
Angle ∠ B = β = 58.67877347743° = 58°40'40″ = 1.02441196694 rad
Angle ∠ C = γ = 72.15444822532° = 72°9'16″ = 1.25993332854 rad

Height: ha = 33.3166018309
Height: hb = 29.50884733594
Height: hc = 26.48219632712

Median: ma = 33.65663515551
Median: mb = 30.57436814924
Median: mc = 26.69773781484

Inradius: r = 9.83661577865
Circumradius: R = 20.48656412813

Vertex coordinates: A[39; 0] B[0; 0] C[16.11553846154; 26.48219632712]
Centroid: CG[18.37217948718; 8.82773210904]
Coordinates of the circumscribed circle: U[19.5; 6.2787857812]
Coordinates of the inscribed circle: I[17.5; 9.83661577865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.8322217027° = 130°49'56″ = 0.85881396988 rad
∠ B' = β' = 121.3222265226° = 121°19'20″ = 1.02441196694 rad
∠ C' = γ' = 107.8465517747° = 107°50'44″ = 1.25993332854 rad

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How did we calculate this triangle?

a = 31 ; ; b = 35 ; ; c = 39 ; ;

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

p = a+b+c = 31+35+39 = 105 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 105 }{ 2 } = 52.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52.5 * (52.5-31)(52.5-35)(52.5-39) } ; ; T = sqrt{ 266667.19 } = 516.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 516.4 }{ 31 } = 33.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 516.4 }{ 35 } = 29.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 516.4 }{ 39 } = 26.48 ; ;

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{ 31**2-35**2-39**2 }{ 2 * 35 * 39 } ) = 49° 10'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-31**2-39**2 }{ 2 * 31 * 39 } ) = 58° 40'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 39**2-31**2-35**2 }{ 2 * 35 * 31 } ) = 72° 9'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 516.4 }{ 52.5 } = 9.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 31 }{ 2 * sin 49° 10'4" } = 20.49 ; ;




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