17 23 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 28

Area: T = 195.3155129982
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 37.3421810948° = 37°20'31″ = 0.65217375497 rad
Angle ∠ B = β = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ C = γ = 87.5088093631° = 87°30'29″ = 1.5277304356 rad

Height: ha = 22.97882505862
Height: hb = 16.98439243463
Height: hc = 13.9511080713

Median: ma = 24.17112639305
Median: mb = 20.10659692629
Median: mc = 14.59545195193

Inradius: r = 5.74545626465
Circumradius: R = 14.01332513044

Vertex coordinates: A[28; 0] B[0; 0] C[9.71442857143; 13.9511080713]
Centroid: CG[12.57114285714; 4.65503602377]
Coordinates of the circumscribed circle: U[14; 0.60992717958]
Coordinates of the inscribed circle: I[11; 5.74545626465]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6588189052° = 142°39'29″ = 0.65217375497 rad
∠ B' = β' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ C' = γ' = 92.4921906369° = 92°29'31″ = 1.5277304356 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 17+23+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-17)(34-23)(34-28) } ; ; T = sqrt{ 38148 } = 195.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195.32 }{ 17 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195.32 }{ 23 } = 16.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195.32 }{ 28 } = 13.95 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 23**2+28**2-17**2 }{ 2 * 23 * 28 } ) = 37° 20'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+28**2-23**2 }{ 2 * 17 * 28 } ) = 55° 9' ; ; gamma = 180° - alpha - beta = 180° - 37° 20'31" - 55° 9' = 87° 30'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195.32 }{ 34 } = 5.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 37° 20'31" } = 14.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 28**2 - 17**2 } }{ 2 } = 24.171 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 17**2 - 23**2 } }{ 2 } = 20.106 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 17**2 - 28**2 } }{ 2 } = 14.595 ; ;
Calculate another triangle

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

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