Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10   b = 25   c = 28

Area: T = 124.1276699384
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 20.77218550453° = 20°46'19″ = 0.36325372623 rad
Angle ∠ B = β = 62.45114540405° = 62°27'5″ = 1.09899834957 rad
Angle ∠ C = γ = 96.77766909142° = 96°46'36″ = 1.68990718956 rad

Height: ha = 24.82553398768
Height: hb = 9.93301359507
Height: hc = 8.86661928132

Median: ma = 26.06772207955
Median: mb = 16.90441415044
Median: mc = 12.90334879006

Inradius: r = 3.94105301392
Circumradius: R = 14.09884978146

Vertex coordinates: A[28; 0] B[0; 0] C[4.625; 8.86661928132]
Centroid: CG[10.875; 2.95553976044]
Coordinates of the circumscribed circle: U[14; -1.66436227421]
Coordinates of the inscribed circle: I[6.5; 3.94105301392]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2288144955° = 159°13'41″ = 0.36325372623 rad
∠ B' = β' = 117.5498545959° = 117°32'55″ = 1.09899834957 rad
∠ C' = γ' = 83.22333090858° = 83°13'24″ = 1.68990718956 rad

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How did we calculate this triangle?

a = 10 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 10+25+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-10)(31.5-25)(31.5-28) } ; ; T = sqrt{ 15407.44 } = 124.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.13 }{ 10 } = 24.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.13 }{ 25 } = 9.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.13 }{ 28 } = 8.87 ; ;

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{ 25**2+28**2-10**2 }{ 2 * 25 * 28 } ) = 20° 46'19" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+28**2-25**2 }{ 2 * 10 * 28 } ) = 62° 27'5" ; ; gamma = 180° - alpha - beta = 180° - 20° 46'19" - 62° 27'5" = 96° 46'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.13 }{ 31.5 } = 3.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 20° 46'19" } = 14.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 28**2 - 10**2 } }{ 2 } = 26.067 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 10**2 - 25**2 } }{ 2 } = 16.904 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 10**2 - 28**2 } }{ 2 } = 12.903 ; ;
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