19 26 30 triangle

Acute scalene triangle.

Sides: a = 19   b = 26   c = 30

Area: T = 244.614385386
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 38.84549485964° = 38°50'42″ = 0.67879722508 rad
Angle ∠ B = β = 59.12655945924° = 59°7'32″ = 1.03219362978 rad
Angle ∠ C = γ = 82.02994568112° = 82°1'46″ = 1.4321684105 rad

Height: ha = 25.74988267221
Height: hb = 18.81664502969
Height: hc = 16.30875902573

Median: ma = 26.41549578837
Median: mb = 21.48325510589
Median: mc = 17.1321841699

Inradius: r = 6.52330361029
Circumradius: R = 15.14663211978

Vertex coordinates: A[30; 0] B[0; 0] C[9.75; 16.30875902573]
Centroid: CG[13.25; 5.43658634191]
Coordinates of the circumscribed circle: U[15; 2.1100248992]
Coordinates of the inscribed circle: I[11.5; 6.52330361029]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.1555051404° = 141°9'18″ = 0.67879722508 rad
∠ B' = β' = 120.8744405408° = 120°52'28″ = 1.03219362978 rad
∠ C' = γ' = 97.97105431888° = 97°58'14″ = 1.4321684105 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 19 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 19+26+30 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-19)(37.5-26)(37.5-30) } ; ; T = sqrt{ 59835.94 } = 244.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 244.61 }{ 19 } = 25.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 244.61 }{ 26 } = 18.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 244.61 }{ 30 } = 16.31 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 19**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 38° 50'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 59° 7'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-26**2 }{ 2 * 26 * 19 } ) = 82° 1'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 244.61 }{ 37.5 } = 6.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 38° 50'42" } = 15.15 ; ;




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