2 6 7 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 6   c = 7

Area: T = 5.56221488653
Perimeter: p = 15
Semiperimeter: s = 7.5

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 52.61768015821° = 52°37' = 0.91883364295 rad
Angle ∠ C = γ = 112.0244312837° = 112°1'28″ = 1.95551931013 rad

Height: ha = 5.56221488653
Height: hb = 1.85440496218
Height: hc = 1.58991853901

Median: ma = 6.44220493634
Median: mb = 4.18333001327
Median: mc = 2.78438821814

Inradius: r = 0.74216198487
Circumradius: R = 3.77655192298

Vertex coordinates: A[7; 0] B[0; 0] C[1.21442857143; 1.58991853901]
Centroid: CG[2.73880952381; 0.53297284634]
Coordinates of the circumscribed circle: U[3.5; -1.41658197112]
Coordinates of the inscribed circle: I[1.5; 0.74216198487]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 127.3833198418° = 127°23' = 0.91883364295 rad
∠ C' = γ' = 67.9765687163° = 67°58'32″ = 1.95551931013 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 = 2 ; ; b = 6 ; ; c = 7 ; ;

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

p = a+b+c = 2+6+7 = 15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15 }{ 2 } = 7.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.5 * (7.5-2)(7.5-6)(7.5-7) } ; ; T = sqrt{ 30.94 } = 5.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.56 }{ 2 } = 5.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.56 }{ 6 } = 1.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.56 }{ 7 } = 1.59 ; ;

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{ 2**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-2**2-7**2 }{ 2 * 2 * 7 } ) = 52° 37' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-2**2-6**2 }{ 2 * 6 * 2 } ) = 112° 1'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.56 }{ 7.5 } = 0.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 15° 21'32" } = 3.78 ; ;




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