Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 145   b = 261.59   c = 299.09

Area: T = 18965.27549996
Perimeter: p = 705.68
Semiperimeter: s = 352.84

Angle ∠ A = α = 298.9996256096° = 28°59'59″ = 0.50661389487 rad
Angle ∠ B = β = 610.9999967543° = 61° = 1.06546507871 rad
Angle ∠ C = γ = 900.0003776361° = 90°1″ = 1.57108029178 rad

Height: ha = 261.5989999994
Height: hb = 1454.999999997
Height: hc = 126.8219853553

Median: ma = 271.4511336523
Median: mb = 195.2765656509
Median: mc = 149.5444164129

Inradius: r = 53.75503542671
Circumradius: R = 149.5455000003

Vertex coordinates: A[299.09; 0] B[0; 0] C[70.29774021198; 126.8219853553]
Centroid: CG[123.129913404; 42.27332845177]
Coordinates of the circumscribed circle: U[149.545; -0.00109856501]
Coordinates of the inscribed circle: I[91.25; 53.75503542671]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1511.00037439° = 151°1″ = 0.50661389487 rad
∠ B' = β' = 1199.000003246° = 119° = 1.06546507871 rad
∠ C' = γ' = 909.9996223639° = 89°59'59″ = 1.57108029178 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 = 145+261.59+299.09 = 705.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 705.68 }{ 2 } = 352.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 352.84 * (352.84-145)(352.84-261.59)(352.84-299.09) } ; ; T = sqrt{ 359681655.81 } = 18965.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18965.27 }{ 145 } = 261.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18965.27 }{ 261.59 } = 145 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18965.27 }{ 299.09 } = 126.82 ; ;

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{ 261.59**2+299.09**2-145**2 }{ 2 * 261.59 * 299.09 } ) = 28° 59'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 145**2+299.09**2-261.59**2 }{ 2 * 145 * 299.09 } ) = 61° ; ; gamma = 180° - alpha - beta = 180° - 28° 59'59" - 61° = 90° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18965.27 }{ 352.84 } = 53.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 145 }{ 2 * sin 28° 59'59" } = 149.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 261.59**2+2 * 299.09**2 - 145**2 } }{ 2 } = 271.451 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 299.09**2+2 * 145**2 - 261.59**2 } }{ 2 } = 195.276 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 261.59**2+2 * 145**2 - 299.09**2 } }{ 2 } = 149.544 ; ;
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