Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 15   b = 22   c = 25

Area: T = 163.6588180364
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 36.521123386° = 36°31'16″ = 0.63774157777 rad
Angle ∠ B = β = 60.79107880662° = 60°47'27″ = 1.06109994066 rad
Angle ∠ C = γ = 82.68879780737° = 82°41'17″ = 1.44331774692 rad

Height: ha = 21.82110907152
Height: hb = 14.87880163967
Height: hc = 13.09326544291

Median: ma = 22.32215142855
Median: mb = 17.43655957742
Median: mc = 14.08801278403

Inradius: r = 5.27992961408
Circumradius: R = 12.60224864471

Vertex coordinates: A[25; 0] B[0; 0] C[7.32; 13.09326544291]
Centroid: CG[10.77333333333; 4.3644218143]
Coordinates of the circumscribed circle: U[12.5; 1.60439528205]
Coordinates of the inscribed circle: I[9; 5.27992961408]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.479876614° = 143°28'44″ = 0.63774157777 rad
∠ B' = β' = 119.2099211934° = 119°12'33″ = 1.06109994066 rad
∠ C' = γ' = 97.31220219263° = 97°18'43″ = 1.44331774692 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+22+25 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-15)(31-22)(31-25) } ; ; T = sqrt{ 26784 } = 163.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 163.66 }{ 15 } = 21.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 163.66 }{ 22 } = 14.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 163.66 }{ 25 } = 13.09 ; ;

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{ 22**2+25**2-15**2 }{ 2 * 22 * 25 } ) = 36° 31'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+25**2-22**2 }{ 2 * 15 * 25 } ) = 60° 47'27" ; ;
 gamma = 180° - alpha - beta = 180° - 36° 31'16" - 60° 47'27" = 82° 41'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 163.66 }{ 31 } = 5.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 36° 31'16" } = 12.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 25**2 - 15**2 } }{ 2 } = 22.322 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 15**2 - 22**2 } }{ 2 } = 17.436 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 15**2 - 25**2 } }{ 2 } = 14.08 ; ;
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