8 10 10 triangle

Acute isosceles triangle.

Sides: a = 8   b = 10   c = 10

Area: T = 36.66106055596
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: ha = 9.16551513899
Height: hb = 7.33221211119
Height: hc = 7.33221211119

Median: ma = 9.16551513899
Median: mb = 7.55498344353
Median: mc = 7.55498344353

Inradius: r = 2.61986146828
Circumradius: R = 5.45554472559

Vertex coordinates: A[10; 0] B[0; 0] C[3.2; 7.33221211119]
Centroid: CG[4.4; 2.44440403706]
Coordinates of the circumscribed circle: U[5; 2.18221789024]
Coordinates of the inscribed circle: I[4; 2.61986146828]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 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 = 10 ; ; c = 10 ; ;

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

p = a+b+c = 8+10+10 = 28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28 }{ 2 } = 14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14 * (14-8)(14-10)(14-10) } ; ; T = sqrt{ 1344 } = 36.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.66 }{ 8 } = 9.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.66 }{ 10 } = 7.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.66 }{ 10 } = 7.33 ; ;

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**2-10**2-10**2 }{ 2 * 10 * 10 } ) = 47° 9'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-8**2-10**2 }{ 2 * 8 * 10 } ) = 66° 25'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-8**2-10**2 }{ 2 * 10 * 8 } ) = 66° 25'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.66 }{ 14 } = 2.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 47° 9'23" } = 5.46 ; ;




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