17 19 28 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 19   c = 28

Area: T = 157.9877341265
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 36.43769168605° = 36°26'13″ = 0.63659441685 rad
Angle ∠ B = β = 41.59112771434° = 41°35'29″ = 0.72659047263 rad
Angle ∠ C = γ = 101.9721805996° = 101°58'19″ = 1.78797437588 rad

Height: ha = 18.58767460312
Height: hb = 16.6330246449
Height: hc = 11.28548100904

Median: ma = 22.36662692463
Median: mb = 21.12546301743
Median: mc = 11.35878166916

Inradius: r = 4.93771044145
Circumradius: R = 14.31112731811

Vertex coordinates: A[28; 0] B[0; 0] C[12.71442857143; 11.28548100904]
Centroid: CG[13.57114285714; 3.76216033635]
Coordinates of the circumscribed circle: U[14; -2.96985922698]
Coordinates of the inscribed circle: I[13; 4.93771044145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5633083139° = 143°33'47″ = 0.63659441685 rad
∠ B' = β' = 138.4098722857° = 138°24'31″ = 0.72659047263 rad
∠ C' = γ' = 78.02881940039° = 78°1'41″ = 1.78797437588 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 = 17 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 17+19+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-19)(32-28) } ; ; T = sqrt{ 24960 } = 157.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 157.99 }{ 17 } = 18.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 157.99 }{ 19 } = 16.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 157.99 }{ 28 } = 11.28 ; ;

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{ 17**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 36° 26'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 41° 35'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-19**2 }{ 2 * 19 * 17 } ) = 101° 58'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 157.99 }{ 32 } = 4.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 36° 26'13" } = 14.31 ; ;




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

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