7 14 14 triangle

Acute isosceles triangle.

Sides: a = 7   b = 14   c = 14

Area: T = 47.4444045991
Perimeter: p = 35
Semiperimeter: s = 17.5

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 = 13.55554417117
Height: hb = 6.77877208559
Height: hc = 6.77877208559

Median: ma = 13.55554417117
Median: mb = 8.57332140997
Median: mc = 8.57332140997

Inradius: r = 2.71110883423
Circumradius: R = 7.23295689129

Vertex coordinates: A[14; 0] B[0; 0] C[1.75; 6.77877208559]
Centroid: CG[5.25; 2.25992402853]
Coordinates of the circumscribed circle: U[7; 1.80773922282]
Coordinates of the inscribed circle: I[3.5; 2.71110883423]

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 = 7 ; ; b = 14 ; ; c = 14 ; ;

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

p = a+b+c = 7+14+14 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-7)(17.5-14)(17.5-14) } ; ; T = sqrt{ 2250.94 } = 47.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.44 }{ 7 } = 13.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.44 }{ 14 } = 6.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.44 }{ 14 } = 6.78 ; ;

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**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-14**2 }{ 2 * 7 * 14 } ) = 75° 31'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 75° 31'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.44 }{ 17.5 } = 2.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 28° 57'18" } = 7.23 ; ;




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