7 16 16 triangle

Acute isosceles triangle.

Sides: a = 7   b = 16   c = 16

Area: T = 54.6443732486
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 25.2711250186° = 25°16'16″ = 0.44110665218 rad
Angle ∠ B = β = 77.3644374907° = 77°21'52″ = 1.35502630659 rad
Angle ∠ C = γ = 77.3644374907° = 77°21'52″ = 1.35502630659 rad

Height: ha = 15.6122494996
Height: hb = 6.83304665607
Height: hc = 6.83304665607

Median: ma = 15.6122494996
Median: mb = 9.40774438611
Median: mc = 9.40774438611

Inradius: r = 2.80222426916
Circumradius: R = 8.19985614748

Vertex coordinates: A[16; 0] B[0; 0] C[1.531125; 6.83304665607]
Centroid: CG[5.844375; 2.27768221869]
Coordinates of the circumscribed circle: U[8; 1.79334353226]
Coordinates of the inscribed circle: I[3.5; 2.80222426916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.7298749814° = 154°43'44″ = 0.44110665218 rad
∠ B' = β' = 102.6365625093° = 102°38'8″ = 1.35502630659 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 = 7 ; ; b = 16 ; ; c = 16 ; ;

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

p = a+b+c = 7+16+16 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-7)(19.5-16)(19.5-16) } ; ; T = sqrt{ 2985.94 } = 54.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.64 }{ 7 } = 15.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.64 }{ 16 } = 6.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.64 }{ 16 } = 6.83 ; ;

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**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 25° 16'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-7**2-16**2 }{ 2 * 7 * 16 } ) = 77° 21'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-7**2-16**2 }{ 2 * 16 * 7 } ) = 77° 21'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.64 }{ 19.5 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 25° 16'16" } = 8.2 ; ;




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