17 23 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 23   c = 30

Area: T = 194.4222220952
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 34.30111527568° = 34°18'4″ = 0.59986680528 rad
Angle ∠ B = β = 49.687978493° = 49°40'47″ = 0.86770758187 rad
Angle ∠ C = γ = 96.01990623132° = 96°1'9″ = 1.6765848782 rad

Height: ha = 22.8733202465
Height: hb = 16.90662800828
Height: hc = 12.96114813968

Median: ma = 25.34326517949
Median: mb = 21.5
Median: mc = 13.56546599663

Inradius: r = 5.55549205986
Circumradius: R = 15.08331524588

Vertex coordinates: A[30; 0] B[0; 0] C[11; 12.96114813968]
Centroid: CG[13.66766666667; 4.32204937989]
Coordinates of the circumscribed circle: U[15; -1.58216093371]
Coordinates of the inscribed circle: I[12; 5.55549205986]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.6998847243° = 145°41'56″ = 0.59986680528 rad
∠ B' = β' = 130.322021507° = 130°19'13″ = 0.86770758187 rad
∠ C' = γ' = 83.98109376868° = 83°58'51″ = 1.6765848782 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 = 30 ; ;

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

p = a+b+c = 17+23+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-17)(35-23)(35-30) } ; ; T = sqrt{ 37800 } = 194.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.42 }{ 17 } = 22.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.42 }{ 23 } = 16.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.42 }{ 30 } = 12.96 ; ;

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**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 34° 18'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 49° 40'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 96° 1'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.42 }{ 35 } = 5.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 18'4" } = 15.08 ; ;




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

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