3.5 3.9 2.2 triangle

Acute scalene triangle.

Sides: a = 3.5   b = 3.9   c = 2.2

Area: T = 3.82112039987
Perimeter: p = 9.6
Semiperimeter: s = 4.8

Angle ∠ A = α = 62.96443082106° = 62°57'52″ = 1.09989344895 rad
Angle ∠ B = β = 82.98879594194° = 82°59'17″ = 1.44884131314 rad
Angle ∠ C = γ = 34.048773237° = 34°2'52″ = 0.59442450327 rad

Height: ha = 2.18435451421
Height: hb = 1.96595917942
Height: hc = 3.4743821817

Median: ma = 2.63986549604
Median: mb = 2.1787728174
Median: mc = 3.53883612026

Inradius: r = 0.79660841664
Circumradius: R = 1.96546948979

Vertex coordinates: A[2.2; 0] B[0; 0] C[0.42772727273; 3.4743821817]
Centroid: CG[0.87657575758; 1.15879406057]
Coordinates of the circumscribed circle: U[1.1; 1.62878900582]
Coordinates of the inscribed circle: I[0.9; 0.79660841664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.0365691789° = 117°2'8″ = 1.09989344895 rad
∠ B' = β' = 97.01220405806° = 97°43″ = 1.44884131314 rad
∠ C' = γ' = 145.952226763° = 145°57'8″ = 0.59442450327 rad

Calculate another triangle




How did we calculate this triangle?

a = 3.5 ; ; b = 3.9 ; ; c = 2.2 ; ;

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

p = a+b+c = 3.5+3.9+2.2 = 9.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9.6 }{ 2 } = 4.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.8 * (4.8-3.5)(4.8-3.9)(4.8-2.2) } ; ; T = sqrt{ 14.6 } = 3.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.82 }{ 3.5 } = 2.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.82 }{ 3.9 } = 1.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.82 }{ 2.2 } = 3.47 ; ;

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{ 3.5**2-3.9**2-2.2**2 }{ 2 * 3.9 * 2.2 } ) = 62° 57'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.9**2-3.5**2-2.2**2 }{ 2 * 3.5 * 2.2 } ) = 82° 59'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.2**2-3.5**2-3.9**2 }{ 2 * 3.9 * 3.5 } ) = 34° 2'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.82 }{ 4.8 } = 0.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 62° 57'52" } = 1.96 ; ;




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

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