Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 8   b = 24   c = 24

Area: T = 94.65772765296
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 23.66443191324
Height: hb = 7.88881063775
Height: hc = 7.88881063775

Median: ma = 23.66443191324
Median: mb = 13.26664991614
Median: mc = 13.26664991614

Inradius: r = 3.38106170189
Circumradius: R = 12.17702212681

Vertex coordinates: A[24; 0] B[0; 0] C[1.33333333333; 7.88881063775]
Centroid: CG[8.44444444444; 2.62993687925]
Coordinates of the circumscribed circle: U[12; 2.02883702113]
Coordinates of the inscribed circle: I[4; 3.38106170189]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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 = 8+24+24 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-8)(28-24)(28-24) } ; ; T = sqrt{ 8960 } = 94.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 94.66 }{ 8 } = 23.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 94.66 }{ 24 } = 7.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 94.66 }{ 24 } = 7.89 ; ;

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{ 24**2+24**2-8**2 }{ 2 * 24 * 24 } ) = 19° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+24**2-24**2 }{ 2 * 8 * 24 } ) = 80° 24'21" ; ; gamma = 180° - alpha - beta = 180° - 19° 11'17" - 80° 24'21" = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 94.66 }{ 28 } = 3.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 19° 11'17" } = 12.17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 8**2 } }{ 2 } = 23.664 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 8**2 - 24**2 } }{ 2 } = 13.266 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 8**2 - 24**2 } }{ 2 } = 13.266 ; ;
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