15 16 16 triangle

Acute isosceles triangle.

Sides: a = 15   b = 16   c = 16

Area: T = 1065.999705188
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 55.90663737668° = 55°54'23″ = 0.97657502951 rad
Angle ∠ B = β = 62.04768131166° = 62°2'49″ = 1.08329211793 rad
Angle ∠ C = γ = 62.04768131166° = 62°2'49″ = 1.08329211793 rad

Height: ha = 14.13332940251
Height: hb = 13.25499631485
Height: hc = 13.25499631485

Median: ma = 14.13332940251
Median: mb = 13.28553302556
Median: mc = 13.28553302556

Inradius: r = 4.51106257527
Circumradius: R = 9.05766289623

Vertex coordinates: A[16; 0] B[0; 0] C[7.031125; 13.25499631485]
Centroid: CG[7.67770833333; 4.41766543828]
Coordinates of the circumscribed circle: U[8; 4.24552948261]
Coordinates of the inscribed circle: I[7.5; 4.51106257527]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 124.0943626233° = 124°5'37″ = 0.97657502951 rad
∠ B' = β' = 117.9533186883° = 117°57'11″ = 1.08329211793 rad
∠ C' = γ' = 117.9533186883° = 117°57'11″ = 1.08329211793 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 = 16 ; ; c = 16 ; ;

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

p = a+b+c = 15+16+16 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-15)(23.5-16)(23.5-16) } ; ; T = sqrt{ 11235.94 } = 106 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106 }{ 15 } = 14.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106 }{ 16 } = 13.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106 }{ 16 } = 13.25 ; ;

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**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 55° 54'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-15**2-16**2 }{ 2 * 15 * 16 } ) = 62° 2'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-15**2-16**2 }{ 2 * 16 * 15 } ) = 62° 2'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106 }{ 23.5 } = 4.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 55° 54'23" } = 9.06 ; ;




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