7 8 8 triangle

Acute isosceles triangle.

Sides: a = 7   b = 8   c = 8

Area: T = 25.17881154974
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 51.88989595447° = 51°53'20″ = 0.90656331895 rad
Angle ∠ B = β = 64.05655202276° = 64°3'20″ = 1.1187979732 rad
Angle ∠ C = γ = 64.05655202276° = 64°3'20″ = 1.1187979732 rad

Height: ha = 7.1943747285
Height: hb = 6.29545288743
Height: hc = 6.29545288743

Median: ma = 7.1943747285
Median: mb = 6.36439610307
Median: mc = 6.36439610307

Inradius: r = 2.18994013476
Circumradius: R = 4.44883074999

Vertex coordinates: A[8; 0] B[0; 0] C[3.06325; 6.29545288743]
Centroid: CG[3.68875; 2.09881762914]
Coordinates of the circumscribed circle: U[4; 1.94661345312]
Coordinates of the inscribed circle: I[3.5; 2.18994013476]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.1111040455° = 128°6'40″ = 0.90656331895 rad
∠ B' = β' = 115.9444479772° = 115°56'40″ = 1.1187979732 rad
∠ C' = γ' = 115.9444479772° = 115°56'40″ = 1.1187979732 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 = 7 ; ; b = 8 ; ; c = 8 ; ;

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

p = a+b+c = 7+8+8 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-7)(11.5-8)(11.5-8) } ; ; T = sqrt{ 633.94 } = 25.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.18 }{ 7 } = 7.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.18 }{ 8 } = 6.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.18 }{ 8 } = 6.29 ; ;

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{ 7**2-8**2-8**2 }{ 2 * 8 * 8 } ) = 51° 53'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-7**2-8**2 }{ 2 * 7 * 8 } ) = 64° 3'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-7**2-8**2 }{ 2 * 8 * 7 } ) = 64° 3'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.18 }{ 11.5 } = 2.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 51° 53'20" } = 4.45 ; ;




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