14 15 24 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 24

Area: T = 97.58881012214
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 32.83105360991° = 32°49'50″ = 0.57330009501 rad
Angle ∠ B = β = 35.51325704274° = 35°30'45″ = 0.62198112798 rad
Angle ∠ C = γ = 111.6576893474° = 111°39'25″ = 1.94987804237 rad

Height: ha = 13.94111573173
Height: hb = 13.01217468295
Height: hc = 8.13223417685

Median: ma = 18.74883332593
Median: mb = 18.15990197973
Median: mc = 8.15547532152

Inradius: r = 3.68325698574
Circumradius: R = 12.91114101436

Vertex coordinates: A[24; 0] B[0; 0] C[11.39658333333; 8.13223417685]
Centroid: CG[11.79986111111; 2.71107805895]
Coordinates of the circumscribed circle: U[12; -4.7654925172]
Coordinates of the inscribed circle: I[11.5; 3.68325698574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.1699463901° = 147°10'10″ = 0.57330009501 rad
∠ B' = β' = 144.4877429573° = 144°29'15″ = 0.62198112798 rad
∠ C' = γ' = 68.34331065264° = 68°20'35″ = 1.94987804237 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 = 14 ; ; b = 15 ; ; c = 24 ; ;

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

p = a+b+c = 14+15+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-14)(26.5-15)(26.5-24) } ; ; T = sqrt{ 9523.44 } = 97.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.59 }{ 14 } = 13.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.59 }{ 15 } = 13.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.59 }{ 24 } = 8.13 ; ;

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{ 14**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 32° 49'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 35° 30'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 111° 39'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.59 }{ 26.5 } = 3.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 32° 49'50" } = 12.91 ; ;




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

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