24.4 13.1 30.3 triangle

Obtuse scalene triangle.

Sides: a = 24.4   b = 13.1   c = 30.3

Area: T = 155.2990386051
Perimeter: p = 67.8
Semiperimeter: s = 33.9

Angle ∠ A = α = 51.48661164389° = 51°29'10″ = 0.89986022509 rad
Angle ∠ B = β = 24.84402554595° = 24°50'25″ = 0.43435442448 rad
Angle ∠ C = γ = 103.6743628102° = 103°40'25″ = 1.80994461579 rad

Height: ha = 12.72987201681
Height: hb = 23.70884558857
Height: hc = 10.25501904984

Median: ma = 19.9
Median: mb = 26.71774568401
Median: mc = 12.40881626359

Inradius: r = 4.58108373466
Circumradius: R = 15.59219053431

Vertex coordinates: A[30.3; 0] B[0; 0] C[22.14325742574; 10.25501904984]
Centroid: CG[17.48108580858; 3.41767301661]
Coordinates of the circumscribed circle: U[15.15; -3.68657851574]
Coordinates of the inscribed circle: I[20.8; 4.58108373466]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5143883561° = 128°30'50″ = 0.89986022509 rad
∠ B' = β' = 155.165974454° = 155°9'35″ = 0.43435442448 rad
∠ C' = γ' = 76.32663718984° = 76°19'35″ = 1.80994461579 rad

Calculate another triangle




How did we calculate this triangle?

a = 24.4 ; ; b = 13.1 ; ; c = 30.3 ; ;

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

p = a+b+c = 24.4+13.1+30.3 = 67.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67.8 }{ 2 } = 33.9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.9 * (33.9-24.4)(33.9-13.1)(33.9-30.3) } ; ; T = sqrt{ 24115.1 } = 155.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 155.29 }{ 24.4 } = 12.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 155.29 }{ 13.1 } = 23.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 155.29 }{ 30.3 } = 10.25 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 24.4**2-13.1**2-30.3**2 }{ 2 * 13.1 * 30.3 } ) = 51° 29'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.1**2-24.4**2-30.3**2 }{ 2 * 24.4 * 30.3 } ) = 24° 50'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30.3**2-24.4**2-13.1**2 }{ 2 * 13.1 * 24.4 } ) = 103° 40'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 155.29 }{ 33.9 } = 4.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.4 }{ 2 * sin 51° 29'10" } = 15.59 ; ;




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