5 8 10 triangle

Obtuse scalene triangle.

Sides: a = 5 b = 8 c = 10

Area: T = 19.81100353357
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 29.68662952314° = 29°41'11″ = 0.51881235945 rad
Angle ∠ B = β = 52.41104970351° = 52°24'38″ = 0.91547357359 rad
Angle ∠ C = γ = 97.90332077335° = 97°54'12″ = 1.70987333232 rad

Height: h_a = 7.92440141343
Height: h_b = 4.95325088339
Height: h_c = 3.96220070671

Median: m_a = 8.70334475928
Median: m_b = 6.81990908485
Median: m_c = 4.41658804332

Inradius: r = 1.72326117683
Circumradius: R = 5.04879465738

Vertex coordinates: A[10; 0] B[0; 0] C[3.05; 3.96220070671]
Centroid: CG[4.35; 1.32106690224]
Coordinates of the circumscribed circle: U[5; -0.69440926539]
Coordinates of the inscribed circle: I[3.5; 1.72326117683]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.3143704769° = 150°18'49″ = 0.51881235945 rad
∠ B' = β' = 127.5989502965° = 127°35'22″ = 0.91547357359 rad
∠ C' = γ' = 82.09767922665° = 82°5'48″ = 1.70987333232 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.

$a = 5 ; ; b = 8 ; ; c = 10 ; ;$

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

$p = a+b+c = 5+8+10 = 23 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-5)(11.5-8)(11.5-10) } ; ; T = sqrt{ 392.44 } = 19.81 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.81 }{ 5 } = 7.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.81 }{ 8 } = 4.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.81 }{ 10 } = 3.96 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 5**2-8**2-10**2 }{ 2 * 8 * 10 } ) = 29° 41'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-5**2-10**2 }{ 2 * 5 * 10 } ) = 52° 24'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-5**2-8**2 }{ 2 * 8 * 5 } ) = 97° 54'12" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.81 }{ 11.5 } = 1.72 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 29° 41'11" } = 5.05 ; ;$

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