13 14 18 triangle

Acute scalene triangle.

Sides: a = 13   b = 14   c = 18

Area: T = 90.42108908383
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 45.85988345181° = 45°51'32″ = 0.88003876535 rad
Angle ∠ B = β = 50.60985359027° = 50°36'31″ = 0.88332855811 rad
Angle ∠ C = γ = 83.53326295792° = 83°31'57″ = 1.4587919419 rad

Height: ha = 13.91109062828
Height: hb = 12.91772701198
Height: hc = 10.04767656487

Median: ma = 14.75663545634
Median: mb = 14.05334693226
Median: mc = 10.07547208398

Inradius: r = 4.01987062595
Circumradius: R = 9.05876413526

Vertex coordinates: A[18; 0] B[0; 0] C[8.25; 10.04767656487]
Centroid: CG[8.75; 3.34989218829]
Coordinates of the circumscribed circle: U[9; 1.02202288337]
Coordinates of the inscribed circle: I[8.5; 4.01987062595]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.1411165482° = 134°8'28″ = 0.88003876535 rad
∠ B' = β' = 129.3911464097° = 129°23'29″ = 0.88332855811 rad
∠ C' = γ' = 96.46773704208° = 96°28'3″ = 1.4587919419 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 = 13 ; ; b = 14 ; ; c = 18 ; ;

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

p = a+b+c = 13+14+18 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-13)(22.5-14)(22.5-18) } ; ; T = sqrt{ 8175.94 } = 90.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90.42 }{ 13 } = 13.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90.42 }{ 14 } = 12.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90.42 }{ 18 } = 10.05 ; ;

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{ 13**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 45° 51'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 50° 36'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-13**2-14**2 }{ 2 * 14 * 13 } ) = 83° 31'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90.42 }{ 22.5 } = 4.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 45° 51'32" } = 9.06 ; ;




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

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