8 26 27 triangle

Acute scalene triangle.

Sides: a = 8   b = 26   c = 27

Area: T = 103.9643635469
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 17.22990702856° = 17°13'45″ = 0.30107040035 rad
Angle ∠ B = β = 74.2866138952° = 74°17'10″ = 1.29765377133 rad
Angle ∠ C = γ = 88.48547907624° = 88°29'5″ = 1.54443509367 rad

Height: ha = 25.99109088673
Height: hb = 7.99772027284
Height: hc = 7.70110100348

Median: ma = 26.20111450131
Median: mb = 15.0833103129
Median: mc = 13.7022189606

Inradius: r = 3.40986437859
Circumradius: R = 13.50547220469

Vertex coordinates: A[27; 0] B[0; 0] C[2.16766666667; 7.70110100348]
Centroid: CG[9.72222222222; 2.56770033449]
Coordinates of the circumscribed circle: U[13.5; 0.35770960157]
Coordinates of the inscribed circle: I[4.5; 3.40986437859]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.7710929714° = 162°46'15″ = 0.30107040035 rad
∠ B' = β' = 105.7143861048° = 105°42'50″ = 1.29765377133 rad
∠ C' = γ' = 91.51552092376° = 91°30'55″ = 1.54443509367 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 = 8 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 8+26+27 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-8)(30.5-26)(30.5-27) } ; ; T = sqrt{ 10808.44 } = 103.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.96 }{ 8 } = 25.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.96 }{ 26 } = 8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.96 }{ 27 } = 7.7 ; ;

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{ 8**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 17° 13'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-8**2-27**2 }{ 2 * 8 * 27 } ) = 74° 17'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-8**2-26**2 }{ 2 * 26 * 8 } ) = 88° 29'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.96 }{ 30.5 } = 3.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 17° 13'45" } = 13.5 ; ;




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