Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 11   b = 20   c = 20

Area: T = 105.7598864877
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 31.92440283257° = 31°55'27″ = 0.55771794048 rad
Angle ∠ B = β = 74.03879858372° = 74°2'17″ = 1.29222066244 rad
Angle ∠ C = γ = 74.03879858372° = 74°2'17″ = 1.29222066244 rad

Height: ha = 19.2298884523
Height: hb = 10.57658864877
Height: hc = 10.57658864877

Median: ma = 19.2298884523
Median: mb = 12.66988594593
Median: mc = 12.66988594593

Inradius: r = 4.14774064658
Circumradius: R = 10.40110193498

Vertex coordinates: A[20; 0] B[0; 0] C[3.025; 10.57658864877]
Centroid: CG[7.675; 3.52552954959]
Coordinates of the circumscribed circle: U[10; 2.86602803212]
Coordinates of the inscribed circle: I[5.5; 4.14774064658]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.0765971674° = 148°4'33″ = 0.55771794048 rad
∠ B' = β' = 105.9622014163° = 105°57'43″ = 1.29222066244 rad
∠ C' = γ' = 105.9622014163° = 105°57'43″ = 1.29222066244 rad

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How did we calculate this triangle?

a = 11 ; ; b = 20 ; ; c = 20 ; ;

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

p = a+b+c = 11+20+20 = 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 * (25.5-11)(25.5-20)(25.5-20) } ; ; T = sqrt{ 11184.94 } = 105.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 105.76 }{ 11 } = 19.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 105.76 }{ 20 } = 10.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 105.76 }{ 20 } = 10.58 ; ;

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{ 20**2+20**2-11**2 }{ 2 * 20 * 20 } ) = 31° 55'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+20**2-20**2 }{ 2 * 11 * 20 } ) = 74° 2'17" ; ; gamma = 180° - alpha - beta = 180° - 31° 55'27" - 74° 2'17" = 74° 2'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 105.76 }{ 25.5 } = 4.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 31° 55'27" } = 10.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 20**2 - 11**2 } }{ 2 } = 19.229 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 11**2 - 20**2 } }{ 2 } = 12.669 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 11**2 - 20**2 } }{ 2 } = 12.669 ; ;
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