24.15 12.5 12.5 triangle

Obtuse isosceles triangle.

Sides: a = 24.15   b = 12.5   c = 12.5

Area: T = 39.02436931185
Perimeter: p = 49.15
Semiperimeter: s = 24.575

Angle ∠ A = α = 150.0332857828° = 150°1'58″ = 2.61985673553 rad
Angle ∠ B = β = 14.98435710862° = 14°59'1″ = 0.26215126492 rad
Angle ∠ C = γ = 14.98435710862° = 14°59'1″ = 0.26215126492 rad

Height: ha = 3.23217758276
Height: hb = 6.2443790899
Height: hc = 6.2443790899

Median: ma = 3.23217758276
Median: mb = 18.18444370273
Median: mc = 18.18444370273

Inradius: r = 1.58879427515
Circumradius: R = 24.17440158251

Vertex coordinates: A[12.5; 0] B[0; 0] C[23.32989; 6.2443790899]
Centroid: CG[11.94329666667; 2.0811263633]
Coordinates of the circumscribed circle: U[6.25; 23.3522099287]
Coordinates of the inscribed circle: I[12.075; 1.58879427515]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.96771421723° = 29°58'2″ = 2.61985673553 rad
∠ B' = β' = 165.0166428914° = 165°59″ = 0.26215126492 rad
∠ C' = γ' = 165.0166428914° = 165°59″ = 0.26215126492 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 = 24.15 ; ; b = 12.5 ; ; c = 12.5 ; ;

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

p = a+b+c = 24.15+12.5+12.5 = 49.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49.15 }{ 2 } = 24.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.58 * (24.58-24.15)(24.58-12.5)(24.58-12.5) } ; ; T = sqrt{ 1522.85 } = 39.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.02 }{ 24.15 } = 3.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.02 }{ 12.5 } = 6.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.02 }{ 12.5 } = 6.24 ; ;

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{ 12.5**2+12.5**2-24.15**2 }{ 2 * 12.5 * 12.5 } ) = 150° 1'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.15**2+12.5**2-12.5**2 }{ 2 * 24.15 * 12.5 } ) = 14° 59'1" ; ;
 gamma = 180° - alpha - beta = 180° - 150° 1'58" - 14° 59'1" = 14° 59'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.02 }{ 24.58 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.15 }{ 2 * sin 150° 1'58" } = 24.17 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 12.5**2 - 24.15**2 } }{ 2 } = 3.232 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 24.15**2 - 12.5**2 } }{ 2 } = 18.184 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.5**2+2 * 24.15**2 - 12.5**2 } }{ 2 } = 18.184 ; ;
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