15 15 16 triangle

Acute isosceles triangle.

Sides: a = 15   b = 15   c = 16

Area: T = 101.5098620324
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 57.76990473645° = 57°46'9″ = 1.00882600823 rad
Angle ∠ B = β = 57.76990473645° = 57°46'9″ = 1.00882600823 rad
Angle ∠ C = γ = 64.4621905271° = 64°27'43″ = 1.12550724891 rad

Height: ha = 13.53444827098
Height: hb = 13.53444827098
Height: hc = 12.68985775404

Median: ma = 13.57438719605
Median: mb = 13.57438719605
Median: mc = 12.68985775404

Inradius: r = 4.41334182749
Circumradius: R = 8.86662420702

Vertex coordinates: A[16; 0] B[0; 0] C[8; 12.68985775404]
Centroid: CG[8; 4.23295258468]
Coordinates of the circumscribed circle: U[8; 3.82223354703]
Coordinates of the inscribed circle: I[8; 4.41334182749]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.2310952636° = 122°13'51″ = 1.00882600823 rad
∠ B' = β' = 122.2310952636° = 122°13'51″ = 1.00882600823 rad
∠ C' = γ' = 115.5388094729° = 115°32'17″ = 1.12550724891 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 = 15 ; ; b = 15 ; ; c = 16 ; ;

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

p = a+b+c = 15+15+16 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-15)(23-15)(23-16) } ; ; T = sqrt{ 10304 } = 101.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.51 }{ 15 } = 13.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.51 }{ 15 } = 13.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.51 }{ 16 } = 12.69 ; ;

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{ 15**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 57° 46'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 57° 46'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 64° 27'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.51 }{ 23 } = 4.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 57° 46'9" } = 8.87 ; ;




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