2 7 8 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 7   c = 8

Area: T = 6.43771965948
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 13.2911177243° = 13°17'28″ = 0.23219748044 rad
Angle ∠ B = β = 53.57664263577° = 53°34'35″ = 0.93550850414 rad
Angle ∠ C = γ = 113.1322396399° = 113°7'57″ = 1.97545328078 rad

Height: ha = 6.43771965948
Height: hb = 1.83991990271
Height: hc = 1.60992991487

Median: ma = 7.45498322129
Median: mb = 4.66436895265
Median: mc = 3.24403703492

Inradius: r = 0.75773172464
Circumradius: R = 4.35497195693

Vertex coordinates: A[8; 0] B[0; 0] C[1.18875; 1.60992991487]
Centroid: CG[3.06325; 0.53664330496]
Coordinates of the circumscribed circle: U[4; -1.70988184022]
Coordinates of the inscribed circle: I[1.5; 0.75773172464]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.7098822757° = 166°42'32″ = 0.23219748044 rad
∠ B' = β' = 126.4243573642° = 126°25'25″ = 0.93550850414 rad
∠ C' = γ' = 66.86876036007° = 66°52'3″ = 1.97545328078 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 = 7 ; ; c = 8 ; ;

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

p = a+b+c = 2+7+8 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-2)(8.5-7)(8.5-8) } ; ; T = sqrt{ 41.44 } = 6.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.44 }{ 2 } = 6.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.44 }{ 7 } = 1.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.44 }{ 8 } = 1.61 ; ;

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**2-7**2-8**2 }{ 2 * 7 * 8 } ) = 13° 17'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-2**2-8**2 }{ 2 * 2 * 8 } ) = 53° 34'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-2**2-7**2 }{ 2 * 7 * 2 } ) = 113° 7'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.44 }{ 8.5 } = 0.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 13° 17'28" } = 4.35 ; ;




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