7 21 24 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 24

Area: T = 70.28551335632
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 16.1955116739° = 16°11'42″ = 0.28326581098 rad
Angle ∠ B = β = 56.796617747° = 56°47'46″ = 0.99112802994 rad
Angle ∠ C = γ = 107.0098705791° = 107°31″ = 1.86876542444 rad

Height: ha = 20.08114667323
Height: hb = 6.69438222441
Height: hc = 5.85770944636

Median: ma = 22.27766694099
Median: mb = 14.22114626533
Median: mc = 10.05498756211

Inradius: r = 2.70332743678
Circumradius: R = 12.54988841706

Vertex coordinates: A[24; 0] B[0; 0] C[3.83333333333; 5.85770944636]
Centroid: CG[9.27877777778; 1.95223648212]
Coordinates of the circumscribed circle: U[12; -3.67107620363]
Coordinates of the inscribed circle: I[5; 2.70332743678]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8054883261° = 163°48'18″ = 0.28326581098 rad
∠ B' = β' = 123.204382253° = 123°12'14″ = 0.99112802994 rad
∠ C' = γ' = 72.9911294209° = 72°59'29″ = 1.86876542444 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 = 7 ; ; b = 21 ; ; c = 24 ; ;

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

p = a+b+c = 7+21+24 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-7)(26-21)(26-24) } ; ; T = sqrt{ 4940 } = 70.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.29 }{ 7 } = 20.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.29 }{ 21 } = 6.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.29 }{ 24 } = 5.86 ; ;

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{ 7**2-21**2-24**2 }{ 2 * 21 * 24 } ) = 16° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 56° 47'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-21**2 }{ 2 * 21 * 7 } ) = 107° 31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.29 }{ 26 } = 2.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 11'42" } = 12.55 ; ;




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

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