15 24 24 triangle

Acute isosceles triangle.

Sides: a = 15   b = 24   c = 24

Area: T = 170.9855196728
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 36.42199137286° = 36°25'12″ = 0.63656474079 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 71.79900431357° = 71°47'24″ = 1.25329726229 rad

Height: ha = 22.79880262304
Height: hb = 14.2498766394
Height: hc = 14.2498766394

Median: ma = 22.79880262304
Median: mb = 16.0165617378
Median: mc = 16.0165617378

Inradius: r = 5.42881014834
Circumradius: R = 12.63326725432

Vertex coordinates: A[24; 0] B[0; 0] C[4.68875; 14.2498766394]
Centroid: CG[9.56325; 4.7549588798]
Coordinates of the circumscribed circle: U[12; 3.94877101698]
Coordinates of the inscribed circle: I[7.5; 5.42881014834]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5880086271° = 143°34'48″ = 0.63656474079 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 108.2109956864° = 108°12'36″ = 1.25329726229 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 = 15 ; ; b = 24 ; ; c = 24 ; ;

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

p = a+b+c = 15+24+24 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-15)(31.5-24)(31.5-24) } ; ; T = sqrt{ 29235.94 } = 170.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 170.99 }{ 15 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 170.99 }{ 24 } = 14.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 170.99 }{ 24 } = 14.25 ; ;

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**2-15**2 }{ 2 * 24 * 24 } ) = 36° 25'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+24**2-24**2 }{ 2 * 15 * 24 } ) = 71° 47'24" ; ; gamma = 180° - alpha - beta = 180° - 36° 25'12" - 71° 47'24" = 71° 47'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 170.99 }{ 31.5 } = 5.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15 }{ 2 * sin 36° 25'12" } = 12.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 24**2 - 15**2 } }{ 2 } = 22.798 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 15**2 - 24**2 } }{ 2 } = 16.016 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 15**2 - 24**2 } }{ 2 } = 16.016 ; ;
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