10 15 18 triangle

Acute scalene triangle.

Sides: a = 10   b = 15   c = 18

Area: T = 754.9995833322
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 33.74987759158° = 33°44'56″ = 0.58990272582 rad
Angle ∠ B = β = 56.44222103696° = 56°26'32″ = 0.98551024081 rad
Angle ∠ C = γ = 89.80990137146° = 89°48'32″ = 1.56774629873 rad

Height: ha = 154.9999166664
Height: hb = 10.9999444443
Height: hc = 8.33332870369

Median: ma = 15.79655689989
Median: mb = 12.48799839743
Median: mc = 9.02877350426

Inradius: r = 3.48883527131
Circumradius: R = 99.0000500004

Vertex coordinates: A[18; 0] B[0; 0] C[5.52877777778; 8.33332870369]
Centroid: CG[7.84325925926; 2.77877623456]
Coordinates of the circumscribed circle: U[9; 0.03300001667]
Coordinates of the inscribed circle: I[6.5; 3.48883527131]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.2511224084° = 146°15'4″ = 0.58990272582 rad
∠ B' = β' = 123.558778963° = 123°33'28″ = 0.98551024081 rad
∠ C' = γ' = 90.19109862854° = 90°11'28″ = 1.56774629873 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 = 10 ; ; b = 15 ; ; c = 18 ; ;

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

p = a+b+c = 10+15+18 = 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 * (21.5-10)(21.5-15)(21.5-18) } ; ; T = sqrt{ 5624.94 } = 75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75 }{ 10 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75 }{ 15 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75 }{ 18 } = 8.33 ; ;

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{ 10**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 33° 44'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 56° 26'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 89° 48'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75 }{ 21.5 } = 3.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 33° 44'56" } = 9 ; ;




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