7 17 19 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 17   c = 19

Area: T = 59.22215121387
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 21.51220360096° = 21°30'43″ = 0.37554558572 rad
Angle ∠ B = β = 62.9422322125° = 62°56'32″ = 1.09985507599 rad
Angle ∠ C = γ = 95.54656418654° = 95°32'44″ = 1.66875860365 rad

Height: ha = 16.92204320396
Height: hb = 6.96772367222
Height: hc = 6.2343843383

Median: ma = 17.68547391838
Median: mb = 11.52217186218
Median: mc = 8.87441196746

Inradius: r = 2.75444889367
Circumradius: R = 9.54546735415

Vertex coordinates: A[19; 0] B[0; 0] C[3.18442105263; 6.2343843383]
Centroid: CG[7.39547368421; 2.07879477943]
Coordinates of the circumscribed circle: U[9.5; -0.92223844179]
Coordinates of the inscribed circle: I[4.5; 2.75444889367]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.488796399° = 158°29'17″ = 0.37554558572 rad
∠ B' = β' = 117.0587677875° = 117°3'28″ = 1.09985507599 rad
∠ C' = γ' = 84.45443581346° = 84°27'16″ = 1.66875860365 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 = 7 ; ; b = 17 ; ; c = 19 ; ;

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

p = a+b+c = 7+17+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-7)(21.5-17)(21.5-19) } ; ; T = sqrt{ 3507.19 } = 59.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.22 }{ 7 } = 16.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.22 }{ 17 } = 6.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.22 }{ 19 } = 6.23 ; ;

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{ 17**2+19**2-7**2 }{ 2 * 17 * 19 } ) = 21° 30'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+19**2-17**2 }{ 2 * 7 * 19 } ) = 62° 56'32" ; ; gamma = 180° - alpha - beta = 180° - 21° 30'43" - 62° 56'32" = 95° 32'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.22 }{ 21.5 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 21° 30'43" } = 9.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 19**2 - 7**2 } }{ 2 } = 17.685 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 7**2 - 17**2 } }{ 2 } = 11.522 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 7**2 - 19**2 } }{ 2 } = 8.874 ; ;
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.