8 28 30 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 28   c = 30

Area: T = 111.2432977306
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 96.66554272562° = 96°39'56″ = 1.68771299785 rad

Height: ha = 27.81107443266
Height: hb = 7.94659269505
Height: hc = 7.41661984871

Median: ma = 28.74402157264
Median: mb = 16.91215345253
Median: mc = 14.10767359797

Inradius: r = 3.37109993123
Circumradius: R = 15.10220769192

Vertex coordinates: A[30; 0] B[0; 0] C[3; 7.41661984871]
Centroid: CG[11; 2.47220661624]
Coordinates of the circumscribed circle: U[15; -1.75329196424]
Coordinates of the inscribed circle: I[5; 3.37109993123]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 83.33545727438° = 83°20'4″ = 1.68771299785 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 = 8 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 8+28+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-8)(33-28)(33-30) } ; ; T = sqrt{ 12375 } = 111.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 111.24 }{ 8 } = 27.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 111.24 }{ 28 } = 7.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 111.24 }{ 30 } = 7.42 ; ;

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{ 8**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-8**2-30**2 }{ 2 * 8 * 30 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-8**2-28**2 }{ 2 * 28 * 8 } ) = 96° 39'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 111.24 }{ 33 } = 3.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 21'32" } = 15.1 ; ;




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

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