7 15 21 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 15   c = 21

Area: T = 31.83106063404
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 11.66597348859° = 11°39'35″ = 0.20435007637 rad
Angle ∠ B = β = 25.66325149891° = 25°39'45″ = 0.44878953809 rad
Angle ∠ C = γ = 142.6787750125° = 142°40'40″ = 2.4990196509 rad

Height: ha = 9.09444589544
Height: hb = 4.24440808454
Height: hc = 3.03114863181

Median: ma = 17.90994946886
Median: mb = 13.7398631664
Median: mc = 5.17220402164

Inradius: r = 1.48804933182
Circumradius: R = 17.31882374883

Vertex coordinates: A[21; 0] B[0; 0] C[6.31095238095; 3.03114863181]
Centroid: CG[9.10331746032; 1.01104954394]
Coordinates of the circumscribed circle: U[10.5; -13.77221221931]
Coordinates of the inscribed circle: I[6.5; 1.48804933182]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.3440265114° = 168°20'25″ = 0.20435007637 rad
∠ B' = β' = 154.3377485011° = 154°20'15″ = 0.44878953809 rad
∠ C' = γ' = 37.3222249875° = 37°19'20″ = 2.4990196509 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 = 15 ; ; c = 21 ; ;

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

p = a+b+c = 7+15+21 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-7)(21.5-15)(21.5-21) } ; ; T = sqrt{ 1013.19 } = 31.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.83 }{ 7 } = 9.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.83 }{ 15 } = 4.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.83 }{ 21 } = 3.03 ; ;

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**2-15**2-21**2 }{ 2 * 15 * 21 } ) = 11° 39'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-21**2 }{ 2 * 7 * 21 } ) = 25° 39'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 142° 40'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.83 }{ 21.5 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 11° 39'35" } = 17.32 ; ;




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

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