6 15 15 triangle

Acute isosceles triangle.

Sides: a = 6   b = 15   c = 15

Area: T = 44.09108153701
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 78.46330409672° = 78°27'47″ = 1.3699438406 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 14.69769384567
Height: hb = 5.87987753827
Height: hc = 5.87987753827

Median: ma = 14.69769384567
Median: mb = 8.61768439698
Median: mc = 8.61768439698

Inradius: r = 2.44994897428
Circumradius: R = 7.65546554462

Vertex coordinates: A[15; 0] B[0; 0] C[1.2; 5.87987753827]
Centroid: CG[5.4; 1.96595917942]
Coordinates of the circumscribed circle: U[7.5; 1.53109310892]
Coordinates of the inscribed circle: I[3; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 101.5376959033° = 101°32'13″ = 1.3699438406 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 6 ; ; b = 15 ; ; c = 15 ; ;

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

p = a+b+c = 6+15+15 = 36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36 }{ 2 } = 18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18 * (18-6)(18-15)(18-15) } ; ; T = sqrt{ 1944 } = 44.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.09 }{ 6 } = 14.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.09 }{ 15 } = 5.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.09 }{ 15 } = 5.88 ; ;

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{ 6**2-15**2-15**2 }{ 2 * 15 * 15 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-6**2-15**2 }{ 2 * 6 * 15 } ) = 78° 27'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-6**2-15**2 }{ 2 * 15 * 6 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.09 }{ 18 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 23° 4'26" } = 7.65 ; ;




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