24 29 30 triangle

Acute scalene triangle.

Sides: a = 24   b = 29   c = 30

Area: T = 323.1077470511
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 47.9688410562° = 47°58'6″ = 0.83772067013 rad
Angle ∠ B = β = 63.83440707981° = 63°50'3″ = 1.11441147104 rad
Angle ∠ C = γ = 68.19875186399° = 68°11'51″ = 1.1990271242 rad

Height: ha = 26.92656225426
Height: hb = 22.28332738283
Height: hc = 21.54404980341

Median: ma = 26.95436639439
Median: mb = 22.97328100153
Median: mc = 21.98986334273

Inradius: r = 7.7865722181
Circumradius: R = 16.15656153182

Vertex coordinates: A[30; 0] B[0; 0] C[10.58333333333; 21.54404980341]
Centroid: CG[13.52877777778; 7.18801660114]
Coordinates of the circumscribed circle: U[15; 66.0003255169]
Coordinates of the inscribed circle: I[12.5; 7.7865722181]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.0321589438° = 132°1'54″ = 0.83772067013 rad
∠ B' = β' = 116.1665929202° = 116°9'57″ = 1.11441147104 rad
∠ C' = γ' = 111.802248136° = 111°48'9″ = 1.1990271242 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 = 24 ; ; b = 29 ; ; c = 30 ; ;

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

p = a+b+c = 24+29+30 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-24)(41.5-29)(41.5-30) } ; ; T = sqrt{ 104398.44 } = 323.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 323.11 }{ 24 } = 26.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 323.11 }{ 29 } = 22.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 323.11 }{ 30 } = 21.54 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 47° 58'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 63° 50'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-24**2-29**2 }{ 2 * 29 * 24 } ) = 68° 11'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 323.11 }{ 41.5 } = 7.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 47° 58'6" } = 16.16 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.