7 18 19 triangle

Acute scalene triangle.

Sides: a = 7   b = 18   c = 19

Area: T = 62.92985308902
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 21.59325161782° = 21°35'33″ = 0.37768605011 rad
Angle ∠ B = β = 71.13768864586° = 71°8'13″ = 1.24215728883 rad
Angle ∠ C = γ = 87.27105973632° = 87°16'14″ = 1.52331592642 rad

Height: ha = 17.98795802543
Height: hb = 6.99220589878
Height: hc = 6.62440558832

Median: ma = 18.17327818454
Median: mb = 11.13655287257
Median: mc = 9.81107084352

Inradius: r = 2.86603877677
Circumradius: R = 9.51107893277

Vertex coordinates: A[19; 0] B[0; 0] C[2.26331578947; 6.62440558832]
Centroid: CG[7.08877192982; 2.20880186277]
Coordinates of the circumscribed circle: U[9.5; 0.45328947299]
Coordinates of the inscribed circle: I[4; 2.86603877677]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.4077483822° = 158°24'27″ = 0.37768605011 rad
∠ B' = β' = 108.8633113541° = 108°51'47″ = 1.24215728883 rad
∠ C' = γ' = 92.72994026368° = 92°43'46″ = 1.52331592642 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 = 18 ; ; c = 19 ; ;

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

p = a+b+c = 7+18+19 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-7)(22-18)(22-19) } ; ; T = sqrt{ 3960 } = 62.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.93 }{ 7 } = 17.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.93 }{ 18 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.93 }{ 19 } = 6.62 ; ;

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**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 21° 35'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 71° 8'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-18**2 }{ 2 * 18 * 7 } ) = 87° 16'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.93 }{ 22 } = 2.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 21° 35'33" } = 9.51 ; ;




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