7 17 19 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 17   c = 19

Area: T = 59.22215121387
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 21.51220360096° = 21°30'43″ = 0.37554558572 rad
Angle ∠ B = β = 62.9422322125° = 62°56'32″ = 1.09985507599 rad
Angle ∠ C = γ = 95.54656418654° = 95°32'44″ = 1.66875860365 rad

Height: ha = 16.92204320396
Height: hb = 6.96772367222
Height: hc = 6.2343843383

Median: ma = 17.68547391838
Median: mb = 11.52217186218
Median: mc = 8.87441196746

Inradius: r = 2.75444889367
Circumradius: R = 9.54546735415

Vertex coordinates: A[19; 0] B[0; 0] C[3.18442105263; 6.2343843383]
Centroid: CG[7.39547368421; 2.07879477943]
Coordinates of the circumscribed circle: U[9.5; -0.92223844179]
Coordinates of the inscribed circle: I[4.5; 2.75444889367]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.488796399° = 158°29'17″ = 0.37554558572 rad
∠ B' = β' = 117.0587677875° = 117°3'28″ = 1.09985507599 rad
∠ C' = γ' = 84.45443581346° = 84°27'16″ = 1.66875860365 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 = 7 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 7+17+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-7)(21.5-17)(21.5-19) } ; ; T = sqrt{ 3507.19 } = 59.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.22 }{ 7 } = 16.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.22 }{ 17 } = 6.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.22 }{ 19 } = 6.23 ; ;

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{ 7**2-17**2-19**2 }{ 2 * 17 * 19 } ) = 21° 30'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 62° 56'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 95° 32'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.22 }{ 21.5 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 21° 30'43" } = 9.54 ; ;




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