10 17 24 triangle

Obtuse scalene triangle.

Sides: a = 10 b = 17 c = 24

Area: T = 70.98989956261
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ B = β = 36.26988522245° = 36°16'8″ = 0.63330108872 rad
Angle ∠ C = γ = 123.3677012969° = 123°22'1″ = 2.15331605647 rad

Height: h_a = 14.19877991252
Height: h_b = 8.35216465442
Height: h_c = 5.91657496355

Median: m_a = 20.18766292382
Median: m_b = 16.30218403869
Median: m_c = 7.10663352018

Inradius: r = 2.78438821814
Circumradius: R = 14.36884241621

Vertex coordinates: A[24; 0] B[0; 0] C[8.06325; 5.91657496355]
Centroid: CG[10.68875; 1.97219165452]
Coordinates of the circumscribed circle: U[12; -7.90326332892]
Coordinates of the inscribed circle: I[8.5; 2.78438821814]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ B' = β' = 143.7311147776° = 143°43'52″ = 0.63330108872 rad
∠ C' = γ' = 56.63329870308° = 56°37'59″ = 2.15331605647 rad

Calculate another triangle

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.

$a = 10 ; ; b = 17 ; ; c = 24 ; ;$

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

$p = a+b+c = 10+17+24 = 51 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-10)(25.5-17)(25.5-24) } ; ; T = sqrt{ 5039.44 } = 70.99 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 10 } = 14.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 17 } = 8.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 24 } = 5.92 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10**2-17**2-24**2 }{ 2 * 17 * 24 } ) = 20° 21'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-24**2 }{ 2 * 10 * 24 } ) = 36° 16'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 123° 22'1" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 25.5 } = 2.78 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 20° 21'51" } = 14.37 ; ;$

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