Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10   b = 22   c = 29

Area: T = 89.28657071429
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 16.25437888126° = 16°15'14″ = 0.28436821307 rad
Angle ∠ B = β = 38.00774183478° = 38°27″ = 0.66333545904 rad
Angle ∠ C = γ = 125.739879284° = 125°44'20″ = 2.19545559325 rad

Height: ha = 17.85771414286
Height: hb = 8.11768824675
Height: hc = 6.15876349754

Median: ma = 25.24987623459
Median: mb = 18.69549190958
Median: mc = 9.042157066

Inradius: r = 2.92774002342
Circumradius: R = 17.86440014291

Vertex coordinates: A[29; 0] B[0; 0] C[7.87993103448; 6.15876349754]
Centroid: CG[12.29331034483; 2.05325449918]
Coordinates of the circumscribed circle: U[14.5; -10.43442008347]
Coordinates of the inscribed circle: I[8.5; 2.92774002342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7466211187° = 163°44'46″ = 0.28436821307 rad
∠ B' = β' = 141.9932581652° = 141°59'33″ = 0.66333545904 rad
∠ C' = γ' = 54.26112071604° = 54°15'40″ = 2.19545559325 rad

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How did we calculate this triangle?

a = 10 ; ; b = 22 ; ; c = 29 ; ;

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

p = a+b+c = 10+22+29 = 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 * (30.5-10)(30.5-22)(30.5-29) } ; ; T = sqrt{ 7971.94 } = 89.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.29 }{ 10 } = 17.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.29 }{ 22 } = 8.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.29 }{ 29 } = 6.16 ; ;

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+29**2-10**2 }{ 2 * 22 * 29 } ) = 16° 15'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+29**2-22**2 }{ 2 * 10 * 29 } ) = 38° 27" ; ; gamma = 180° - alpha - beta = 180° - 16° 15'14" - 38° 27" = 125° 44'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.29 }{ 30.5 } = 2.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 16° 15'14" } = 17.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 29**2 - 10**2 } }{ 2 } = 25.249 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 10**2 - 22**2 } }{ 2 } = 18.695 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 10**2 - 29**2 } }{ 2 } = 9.042 ; ;
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