11 16 24 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 24

Area: T = 72.58774472619
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 22.21435428093° = 22°12'49″ = 0.38876994606 rad
Angle ∠ B = β = 33.36604891971° = 33°21'38″ = 0.58222503766 rad
Angle ∠ C = γ = 124.4265967994° = 124°25'33″ = 2.17216428165 rad

Height: ha = 13.1987717684
Height: hb = 9.07334309077
Height: hc = 6.04989539385

Median: ma = 19.64105193414
Median: mb = 16.86771277934
Median: mc = 6.67108320321

Inradius: r = 2.84765665593
Circumradius: R = 14.54879699292

Vertex coordinates: A[24; 0] B[0; 0] C[9.18875; 6.04989539385]
Centroid: CG[11.06325; 2.01663179795]
Coordinates of the circumscribed circle: U[12; -8.22545625452]
Coordinates of the inscribed circle: I[9.5; 2.84765665593]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.7866457191° = 157°47'11″ = 0.38876994606 rad
∠ B' = β' = 146.6439510803° = 146°38'22″ = 0.58222503766 rad
∠ C' = γ' = 55.57440320065° = 55°34'27″ = 2.17216428165 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 = 11 ; ; b = 16 ; ; c = 24 ; ;

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

p = a+b+c = 11+16+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 * (25.5-11)(25.5-16)(25.5-24) } ; ; T = sqrt{ 5268.94 } = 72.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.59 }{ 11 } = 13.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.59 }{ 16 } = 9.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.59 }{ 24 } = 6.05 ; ;

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{ 11**2-16**2-24**2 }{ 2 * 16 * 24 } ) = 22° 12'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 33° 21'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 124° 25'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.59 }{ 25.5 } = 2.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 22° 12'49" } = 14.55 ; ;




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

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