Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8   b = 11   c = 15

Area: T = 42.84985705713
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 31.29904452139° = 31°17'26″ = 0.54661212934 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 103.1376558787° = 103°8'12″ = 1.880007253 rad

Height: ha = 10.71221426428
Height: hb = 7.79106491948
Height: hc = 5.71331427428

Median: ma = 12.53299640861
Median: mb = 10.68987791632
Median: mc = 6.02107972894

Inradius: r = 2.52105041513
Circumradius: R = 7.70215404622

Vertex coordinates: A[15; 0] B[0; 0] C[5.6; 5.71331427428]
Centroid: CG[6.86766666667; 1.90443809143]
Coordinates of the circumscribed circle: U[7.5; -1.7550350105]
Coordinates of the inscribed circle: I[6; 2.52105041513]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7109554786° = 148°42'34″ = 0.54661212934 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 76.86334412131° = 76°51'48″ = 1.880007253 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 = 8+11+15 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-8)(17-11)(17-15) } ; ; T = sqrt{ 1836 } = 42.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.85 }{ 8 } = 10.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.85 }{ 11 } = 7.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.85 }{ 15 } = 5.71 ; ;

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{ 11**2+15**2-8**2 }{ 2 * 11 * 15 } ) = 31° 17'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+15**2-11**2 }{ 2 * 8 * 15 } ) = 45° 34'23" ; ;
 gamma = 180° - alpha - beta = 180° - 31° 17'26" - 45° 34'23" = 103° 8'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.85 }{ 17 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 31° 17'26" } = 7.7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 15**2 - 8**2 } }{ 2 } = 12.53 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 8**2 - 11**2 } }{ 2 } = 10.689 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 8**2 - 15**2 } }{ 2 } = 6.021 ; ;
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