8 8 10 triangle

Acute isosceles triangle.

Sides: a = 8   b = 8   c = 10

Area: T = 31.2254989992
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 77.3644374907° = 77°21'52″ = 1.35502630659 rad

Height: ha = 7.8066247498
Height: hb = 7.8066247498
Height: hc = 6.24549979984

Median: ma = 8.12440384046
Median: mb = 8.12440384046
Median: mc = 6.24549979984

Inradius: r = 2.40219223071
Circumradius: R = 5.12441009218

Vertex coordinates: A[10; 0] B[0; 0] C[5; 6.24549979984]
Centroid: CG[5; 2.08216659995]
Coordinates of the circumscribed circle: U[5; 1.12108970766]
Coordinates of the inscribed circle: I[5; 2.40219223071]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 102.6365625093° = 102°38'8″ = 1.35502630659 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 = 8 ; ; c = 10 ; ;

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

p = a+b+c = 8+8+10 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-8)(13-8)(13-10) } ; ; T = sqrt{ 975 } = 31.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.22 }{ 8 } = 7.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.22 }{ 8 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.22 }{ 10 } = 6.24 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 8**2+10**2-8**2 }{ 2 * 8 * 10 } ) = 51° 19'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+10**2-8**2 }{ 2 * 8 * 10 } ) = 51° 19'4" ; ; gamma = 180° - alpha - beta = 180° - 51° 19'4" - 51° 19'4" = 77° 21'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.22 }{ 13 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 51° 19'4" } = 5.12 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 10**2 - 8**2 } }{ 2 } = 8.124 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 8**2 - 8**2 } }{ 2 } = 8.124 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 10**2 } }{ 2 } = 6.245 ; ;
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