3 15 15 triangle

Acute isosceles triangle.

Sides: a = 3   b = 15   c = 15

Area: T = 22.38772173349
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 84.26108295227° = 84°15'39″ = 1.47106289056 rad
Angle ∠ C = γ = 84.26108295227° = 84°15'39″ = 1.47106289056 rad

Height: ha = 14.92548115566
Height: hb = 2.98549623113
Height: hc = 2.98549623113

Median: ma = 14.92548115566
Median: mb = 7.79442286341
Median: mc = 7.79442286341

Inradius: r = 1.35768010506
Circumradius: R = 7.53877836144

Vertex coordinates: A[15; 0] B[0; 0] C[0.3; 2.98549623113]
Centroid: CG[5.1; 0.99549874371]
Coordinates of the circumscribed circle: U[7.5; 0.75437783614]
Coordinates of the inscribed circle: I[1.5; 1.35768010506]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 95.73991704773° = 95°44'21″ = 1.47106289056 rad
∠ C' = γ' = 95.73991704773° = 95°44'21″ = 1.47106289056 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 = 3 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 3+15+15 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-3)(16.5-15)(16.5-15) } ; ; T = sqrt{ 501.19 } = 22.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.39 }{ 3 } = 14.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.39 }{ 15 } = 2.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.39 }{ 15 } = 2.98 ; ;

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{ 3**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-3**2-15**2 }{ 2 * 3 * 15 } ) = 84° 15'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-3**2-15**2 }{ 2 * 15 * 3 } ) = 84° 15'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.39 }{ 16.5 } = 1.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 11° 28'42" } = 7.54 ; ;




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