23 28 30 triangle

Acute scalene triangle.

Sides: a = 23   b = 28   c = 30

Area: T = 304.9977438514
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ B = β = 62.13549067337° = 62°8'6″ = 1.08444587029 rad
Angle ∠ C = γ = 71.29876298241° = 71°17'51″ = 1.24443783893 rad

Height: ha = 26.52215163925
Height: hb = 21.78655313224
Height: hc = 20.33331625676

Median: ma = 26.64111336095
Median: mb = 22.77105950735
Median: mc = 20.77325780778

Inradius: r = 7.5310800951
Circumradius: R = 15.83661985712

Vertex coordinates: A[30; 0] B[0; 0] C[10.75; 20.33331625676]
Centroid: CG[13.58333333333; 6.77877208559]
Coordinates of the circumscribed circle: U[15; 5.07879114984]
Coordinates of the inscribed circle: I[12.5; 7.5310800951]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ B' = β' = 117.8655093266° = 117°51'54″ = 1.08444587029 rad
∠ C' = γ' = 108.7022370176° = 108°42'9″ = 1.24443783893 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 = 23 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 23+28+30 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-23)(40.5-28)(40.5-30) } ; ; T = sqrt{ 93023.44 } = 305 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 305 }{ 23 } = 26.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 305 }{ 28 } = 21.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 305 }{ 30 } = 20.33 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 28**2+30**2-23**2 }{ 2 * 28 * 30 } ) = 46° 34'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 23**2+30**2-28**2 }{ 2 * 23 * 30 } ) = 62° 8'6" ; ; gamma = 180° - alpha - beta = 180° - 46° 34'3" - 62° 8'6" = 71° 17'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 305 }{ 40.5 } = 7.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 23 }{ 2 * sin 46° 34'3" } = 15.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 30**2 - 23**2 } }{ 2 } = 26.641 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 23**2 - 28**2 } }{ 2 } = 22.771 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 23**2 - 30**2 } }{ 2 } = 20.773 ; ;
Calculate another triangle

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

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