3.1 4.5 5.2 triangle

Acute scalene triangle.

Sides: a = 3.1   b = 4.5   c = 5.2

Area: T = 6.93992795015
Perimeter: p = 12.8
Semiperimeter: s = 6.4

Angle ∠ A = α = 36.37773613942° = 36°22'38″ = 0.63549047295 rad
Angle ∠ B = β = 59.42437311947° = 59°25'25″ = 1.03771397632 rad
Angle ∠ C = γ = 84.19989074111° = 84°11'56″ = 1.47695481609 rad

Height: ha = 4.47769545171
Height: hb = 3.08441242229
Height: hc = 2.66989536544

Median: ma = 4.60989586676
Median: mb = 3.64217715469
Median: mc = 2.85883211856

Inradius: r = 1.08442624221
Circumradius: R = 2.61333837088

Vertex coordinates: A[5.2; 0] B[0; 0] C[1.57769230769; 2.66989536544]
Centroid: CG[2.2598974359; 0.89896512181]
Coordinates of the circumscribed circle: U[2.6; 0.26441484609]
Coordinates of the inscribed circle: I[1.9; 1.08442624221]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.6232638606° = 143°37'22″ = 0.63549047295 rad
∠ B' = β' = 120.5766268805° = 120°34'35″ = 1.03771397632 rad
∠ C' = γ' = 95.80110925889° = 95°48'4″ = 1.47695481609 rad

Calculate another triangle




How did we calculate this triangle?

a = 3.1 ; ; b = 4.5 ; ; c = 5.2 ; ;

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

p = a+b+c = 3.1+4.5+5.2 = 12.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.8 }{ 2 } = 6.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.4 * (6.4-3.1)(6.4-4.5)(6.4-5.2) } ; ; T = sqrt{ 48.15 } = 6.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.94 }{ 3.1 } = 4.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.94 }{ 4.5 } = 3.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.94 }{ 5.2 } = 2.67 ; ;

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{ 3.1**2-4.5**2-5.2**2 }{ 2 * 4.5 * 5.2 } ) = 36° 22'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.5**2-3.1**2-5.2**2 }{ 2 * 3.1 * 5.2 } ) = 59° 25'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.2**2-3.1**2-4.5**2 }{ 2 * 4.5 * 3.1 } ) = 84° 11'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.94 }{ 6.4 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.1 }{ 2 * sin 36° 22'38" } = 2.61 ; ;




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

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