13 14 17 triangle

Acute scalene triangle.

Sides: a = 13   b = 14   c = 17

Area: T = 88.99443818451
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 48.40546480534° = 48°24'17″ = 0.84548204818 rad
Angle ∠ B = β = 53.64768753478° = 53°38'49″ = 0.93663146082 rad
Angle ∠ C = γ = 77.94884765988° = 77°56'55″ = 1.36604575636 rad

Height: ha = 13.69114433608
Height: hb = 12.71334831207
Height: hc = 10.47699272759

Median: ma = 14.15109716981
Median: mb = 13.4166407865
Median: mc = 10.5

Inradius: r = 4.04551991748
Circumradius: R = 8.69215598936

Vertex coordinates: A[17; 0] B[0; 0] C[7.70658823529; 10.47699272759]
Centroid: CG[8.23552941176; 3.49899757586]
Coordinates of the circumscribed circle: U[8.5; 1.81547212965]
Coordinates of the inscribed circle: I[8; 4.04551991748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.5955351947° = 131°35'43″ = 0.84548204818 rad
∠ B' = β' = 126.3533124652° = 126°21'11″ = 0.93663146082 rad
∠ C' = γ' = 102.0521523401° = 102°3'5″ = 1.36604575636 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 = 17 ; ;

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

p = a+b+c = 13+14+17 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-13)(22-14)(22-17) } ; ; T = sqrt{ 7920 } = 88.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.99 }{ 13 } = 13.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.99 }{ 14 } = 12.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.99 }{ 17 } = 10.47 ; ;

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{ 13**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 48° 24'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-13**2-17**2 }{ 2 * 13 * 17 } ) = 53° 38'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-13**2-14**2 }{ 2 * 14 * 13 } ) = 77° 56'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.99 }{ 22 } = 4.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 48° 24'17" } = 8.69 ; ;




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

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