Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 35   b = 33   c = 25.31

Area: T = 398.106640753
Perimeter: p = 93.31
Semiperimeter: s = 46.655

Angle ∠ A = α = 72.4188016457° = 72°25'5″ = 1.26439328249 rad
Angle ∠ B = β = 64.00223769031° = 64°9″ = 1.11770522061 rad
Angle ∠ C = γ = 43.58796066399° = 43°34'47″ = 0.76106076226 rad

Height: ha = 22.74989375732
Height: hb = 24.12876610624
Height: hc = 31.4588428094

Median: ma = 23.63436211783
Median: mb = 25.70111293526
Median: mc = 31.5732946885

Inradius: r = 8.53329848361
Circumradius: R = 18.35875605963

Vertex coordinates: A[25.31; 0] B[0; 0] C[15.34216851047; 31.4588428094]
Centroid: CG[13.55105617016; 10.4866142698]
Coordinates of the circumscribed circle: U[12.655; 13.29985339811]
Coordinates of the inscribed circle: I[13.655; 8.53329848361]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 107.5821983543° = 107°34'55″ = 1.26439328249 rad
∠ B' = β' = 115.9987623097° = 115°59'51″ = 1.11770522061 rad
∠ C' = γ' = 136.422039336° = 136°25'13″ = 0.76106076226 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 = 35+33+25.31 = 93.31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 93.31 }{ 2 } = 46.66 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 46.66 * (46.66-35)(46.66-33)(46.66-25.31) } ; ; T = sqrt{ 158488.71 } = 398.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 398.11 }{ 35 } = 22.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 398.11 }{ 33 } = 24.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 398.11 }{ 25.31 } = 31.46 ; ;

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{ 33**2+25.31**2-35**2 }{ 2 * 33 * 25.31 } ) = 72° 25'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+25.31**2-33**2 }{ 2 * 35 * 25.31 } ) = 64° 9" ; ; gamma = 180° - alpha - beta = 180° - 72° 25'5" - 64° 9" = 43° 34'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 398.11 }{ 46.66 } = 8.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 72° 25'5" } = 18.36 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 25.31**2 - 35**2 } }{ 2 } = 23.634 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.31**2+2 * 35**2 - 33**2 } }{ 2 } = 25.701 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 35**2 - 25.31**2 } }{ 2 } = 31.573 ; ;
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