Triangle calculator SSS - result

Please enter the triangle sides:


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?

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 15**2+15**2-6**2 }{ 2 * 15 * 15 } ) = 23° 4'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+15**2-15**2 }{ 2 * 6 * 15 } ) = 78° 27'47" ; ; gamma = 180° - alpha - beta = 180° - 23° 4'26" - 78° 27'47" = 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 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 15**2 - 6**2 } }{ 2 } = 14.697 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 6**2 - 15**2 } }{ 2 } = 8.617 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 6**2 - 15**2 } }{ 2 } = 8.617 ; ;
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