Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 100   b = 90   c = 168.69

Area: T = 3680.588009046
Perimeter: p = 358.69
Semiperimeter: s = 179.345

Angle ∠ A = α = 29.00331587566° = 29°11″ = 0.50662006138 rad
Angle ∠ B = β = 25.87326319918° = 25°52'21″ = 0.45215626144 rad
Angle ∠ C = γ = 125.1244209252° = 125°7'27″ = 2.18438294254 rad

Height: ha = 73.61216018092
Height: hb = 81.79106686769
Height: hc = 43.63772054118

Median: ma = 125.611113824
Median: mb = 131.1610809886
Median: mc = 43.99991019795

Inradius: r = 20.5222345705
Circumradius: R = 103.1233010686

Vertex coordinates: A[168.69; 0] B[0; 0] C[89.97766319877; 43.63772054118]
Centroid: CG[86.22222106626; 14.54657351373]
Coordinates of the circumscribed circle: U[84.345; -59.33219164361]
Coordinates of the inscribed circle: I[89.345; 20.5222345705]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.9976841243° = 150°59'49″ = 0.50662006138 rad
∠ B' = β' = 154.1277368008° = 154°7'39″ = 0.45215626144 rad
∠ C' = γ' = 54.87657907485° = 54°52'33″ = 2.18438294254 rad

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How did we calculate this triangle?

a = 100 ; ; b = 90 ; ; c = 168.69 ; ;

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

p = a+b+c = 100+90+168.69 = 358.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 358.69 }{ 2 } = 179.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 179.35 * (179.35-100)(179.35-90)(179.35-168.69) } ; ; T = sqrt{ 13546669.8 } = 3680.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3680.58 }{ 100 } = 73.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3680.58 }{ 90 } = 81.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3680.58 }{ 168.69 } = 43.64 ; ;

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{ 90**2+168.69**2-100**2 }{ 2 * 90 * 168.69 } ) = 29° 11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+168.69**2-90**2 }{ 2 * 100 * 168.69 } ) = 25° 52'21" ; ; gamma = 180° - alpha - beta = 180° - 29° 11" - 25° 52'21" = 125° 7'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3680.58 }{ 179.35 } = 20.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 29° 11" } = 103.12 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 168.69**2 - 100**2 } }{ 2 } = 125.611 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 168.69**2+2 * 100**2 - 90**2 } }{ 2 } = 131.161 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 168.69**2 } }{ 2 } = 43.999 ; ;
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