6 27 30 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 27   c = 30

Area: T = 73.63438067738
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 10.47553138432° = 10°28'31″ = 0.18328287167 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 114.6244318352° = 114°37'28″ = 2.00105717581 rad

Height: ha = 24.54546022579
Height: hb = 5.45443560573
Height: hc = 4.90989204516

Median: ma = 28.38113318926
Median: mb = 16.90441415044
Median: mc = 12.5549900398

Inradius: r = 2.33875811674
Circumradius: R = 16.50105729465

Vertex coordinates: A[30; 0] B[0; 0] C[3.45; 4.90989204516]
Centroid: CG[11.15; 1.63663068172]
Coordinates of the circumscribed circle: U[15; -6.87552387277]
Coordinates of the inscribed circle: I[4.5; 2.33875811674]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5254686157° = 169°31'29″ = 0.18328287167 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 65.37656816478° = 65°22'32″ = 2.00105717581 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 = 6 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 6+27+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-6)(31.5-27)(31.5-30) } ; ; T = sqrt{ 5421.94 } = 73.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.63 }{ 6 } = 24.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.63 }{ 27 } = 5.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.63 }{ 30 } = 4.91 ; ;

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{ 6**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 10° 28'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-6**2-30**2 }{ 2 * 6 * 30 } ) = 54° 54'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-6**2-27**2 }{ 2 * 27 * 6 } ) = 114° 37'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.63 }{ 31.5 } = 2.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 10° 28'31" } = 16.5 ; ;




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