15 18 18 triangle

Acute isosceles triangle.

Sides: a = 15   b = 18   c = 18

Area: T = 122.723301129
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 49.24986367043° = 49°14'55″ = 0.86595508626 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 65.37656816478° = 65°22'32″ = 1.14110208955 rad

Height: ha = 16.3633068172
Height: hb = 13.63658901433
Height: hc = 13.63658901433

Median: ma = 16.3633068172
Median: mb = 13.91104277432
Median: mc = 13.91104277432

Inradius: r = 4.81326671094
Circumradius: R = 9.99003437679

Vertex coordinates: A[18; 0] B[0; 0] C[6.25; 13.63658901433]
Centroid: CG[8.08333333333; 4.54552967144]
Coordinates of the circumscribed circle: U[9; 4.12551432366]
Coordinates of the inscribed circle: I[7.5; 4.81326671094]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.7511363296° = 130°45'5″ = 0.86595508626 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 114.6244318352° = 114°37'28″ = 1.14110208955 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 = 18 ; ; c = 18 ; ;

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

p = a+b+c = 15+18+18 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-15)(25.5-18)(25.5-18) } ; ; T = sqrt{ 15060.94 } = 122.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 122.72 }{ 15 } = 16.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 122.72 }{ 18 } = 13.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 122.72 }{ 18 } = 13.64 ; ;

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**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 49° 14'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 65° 22'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 65° 22'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 122.72 }{ 25.5 } = 4.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 49° 14'55" } = 9.9 ; ;




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