4 21 24 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 21   c = 24

Area: T = 29.64768801057
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 6.75662861124° = 6°45'23″ = 0.11879194379 rad
Angle ∠ B = β = 38.14442418483° = 38°8'39″ = 0.66657426109 rad
Angle ∠ C = γ = 135.0999472039° = 135°5'58″ = 2.35879306048 rad

Height: ha = 14.82334400528
Height: hb = 2.8243512391
Height: hc = 2.47105733421

Median: ma = 22.46110774452
Median: mb = 13.62990131704
Median: mc = 9.19223881554

Inradius: r = 1.2110076739
Circumradius: R = 177.0001024797

Vertex coordinates: A[24; 0] B[0; 0] C[3.14658333333; 2.47105733421]
Centroid: CG[9.04986111111; 0.82435244474]
Coordinates of the circumscribed circle: U[12; -12.04217392565]
Coordinates of the inscribed circle: I[3.5; 1.2110076739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.2443713888° = 173°14'37″ = 0.11879194379 rad
∠ B' = β' = 141.8565758152° = 141°51'21″ = 0.66657426109 rad
∠ C' = γ' = 44.90105279607° = 44°54'2″ = 2.35879306048 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 = 4 ; ; b = 21 ; ; c = 24 ; ;

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

p = a+b+c = 4+21+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-4)(24.5-21)(24.5-24) } ; ; T = sqrt{ 878.94 } = 29.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.65 }{ 4 } = 14.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.65 }{ 21 } = 2.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.65 }{ 24 } = 2.47 ; ;

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{ 4**2-21**2-24**2 }{ 2 * 21 * 24 } ) = 6° 45'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-4**2-24**2 }{ 2 * 4 * 24 } ) = 38° 8'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-4**2-21**2 }{ 2 * 21 * 4 } ) = 135° 5'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.65 }{ 24.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 6° 45'23" } = 17 ; ;




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

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