8 16 16 triangle

Acute isosceles triangle.

Sides: a = 8   b = 16   c = 16

Area: T = 61.96877335393
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 15.49219333848
Height: hb = 7.74659666924
Height: hc = 7.74659666924

Median: ma = 15.49219333848
Median: mb = 9.79879589711
Median: mc = 9.79879589711

Inradius: r = 3.0988386677
Circumradius: R = 8.26223644719

Vertex coordinates: A[16; 0] B[0; 0] C[2; 7.74659666924]
Centroid: CG[6; 2.58219888975]
Coordinates of the circumscribed circle: U[8; 2.0665591118]
Coordinates of the inscribed circle: I[4; 3.0988386677]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 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 = 16 ; ; c = 16 ; ;

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

p = a+b+c = 8+16+16 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-8)(20-16)(20-16) } ; ; T = sqrt{ 3840 } = 61.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.97 }{ 8 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.97 }{ 16 } = 7.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.97 }{ 16 } = 7.75 ; ;

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**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-8**2-16**2 }{ 2 * 8 * 16 } ) = 75° 31'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-8**2-16**2 }{ 2 * 16 * 8 } ) = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.97 }{ 20 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 28° 57'18" } = 8.26 ; ;




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