Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 15   b = 21   c = 25

Area: T = 157.166611435
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 36.77988554827° = 36°46'44″ = 0.64219121233 rad
Angle ∠ B = β = 56.95325545924° = 56°57'9″ = 0.99440095951 rad
Angle ∠ C = γ = 86.26985899249° = 86°16'7″ = 1.50656709352 rad

Height: ha = 20.95554819134
Height: hb = 14.96882013667
Height: hc = 12.5733289148

Median: ma = 21.83546055609
Median: mb = 17.74111949992
Median: mc = 13.29547358003

Inradius: r = 5.15329873558
Circumradius: R = 12.52765551556

Vertex coordinates: A[25; 0] B[0; 0] C[8.18; 12.5733289148]
Centroid: CG[11.06; 4.19110963827]
Coordinates of the circumscribed circle: U[12.5; 0.81552202562]
Coordinates of the inscribed circle: I[9.5; 5.15329873558]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.2211144517° = 143°13'16″ = 0.64219121233 rad
∠ B' = β' = 123.0477445408° = 123°2'51″ = 0.99440095951 rad
∠ C' = γ' = 93.73114100751° = 93°43'53″ = 1.50656709352 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 = 15+21+25 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-15)(30.5-21)(30.5-25) } ; ; T = sqrt{ 24701.19 } = 157.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 157.17 }{ 15 } = 20.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 157.17 }{ 21 } = 14.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 157.17 }{ 25 } = 12.57 ; ;

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{ 21**2+25**2-15**2 }{ 2 * 21 * 25 } ) = 36° 46'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+25**2-21**2 }{ 2 * 15 * 25 } ) = 56° 57'9" ; ; gamma = 180° - alpha - beta = 180° - 36° 46'44" - 56° 57'9" = 86° 16'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 157.17 }{ 30.5 } = 5.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 36° 46'44" } = 12.53 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 25**2 - 15**2 } }{ 2 } = 21.835 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 15**2 - 21**2 } }{ 2 } = 17.741 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 15**2 - 25**2 } }{ 2 } = 13.295 ; ;
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