18 25 27 triangle

Acute scalene triangle.

Sides: a = 18   b = 25   c = 27

Area: T = 218.1744242293
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 40.274389294° = 40°16'26″ = 0.70329120344 rad
Angle ∠ B = β = 63.87551115689° = 63°52'30″ = 1.1154831007 rad
Angle ∠ C = γ = 75.85109954911° = 75°51'4″ = 1.32438496122 rad

Height: ha = 24.2421582477
Height: hb = 17.45439393834
Height: hc = 16.16110549846

Median: ma = 24.41331112315
Median: mb = 19.24218814049
Median: mc = 17.09553209973

Inradius: r = 6.23435497798
Circumradius: R = 13.92223584236

Vertex coordinates: A[27; 0] B[0; 0] C[7.92659259259; 16.16110549846]
Centroid: CG[11.64219753086; 5.38770183282]
Coordinates of the circumscribed circle: U[13.5; 3.40332431702]
Coordinates of the inscribed circle: I[10; 6.23435497798]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.726610706° = 139°43'34″ = 0.70329120344 rad
∠ B' = β' = 116.1254888431° = 116°7'30″ = 1.1154831007 rad
∠ C' = γ' = 104.1499004509° = 104°8'56″ = 1.32438496122 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 = 18 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 18+25+27 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-18)(35-25)(35-27) } ; ; T = sqrt{ 47600 } = 218.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218.17 }{ 18 } = 24.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218.17 }{ 25 } = 17.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218.17 }{ 27 } = 16.16 ; ;

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{ 18**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 40° 16'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-27**2 }{ 2 * 18 * 27 } ) = 63° 52'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 75° 51'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218.17 }{ 35 } = 6.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 40° 16'26" } = 13.92 ; ;




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