15 17 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 30

Area: T = 83.3310666624
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 19.07438706794° = 19°4'26″ = 0.33329018445 rad
Angle ∠ B = β = 21.73877297313° = 21°44'16″ = 0.37993949557 rad
Angle ∠ C = γ = 139.1888399589° = 139°11'18″ = 2.42992958534 rad

Height: ha = 11.11107555499
Height: hb = 9.80436078381
Height: hc = 5.55553777749

Median: ma = 23.22002155162
Median: mb = 22.14215898255
Median: mc = 5.65768542495

Inradius: r = 2.68880860201
Circumradius: R = 22.95107344353

Vertex coordinates: A[30; 0] B[0; 0] C[13.93333333333; 5.55553777749]
Centroid: CG[14.64444444444; 1.85217925916]
Coordinates of the circumscribed circle: U[15; -17.37105558667]
Coordinates of the inscribed circle: I[14; 2.68880860201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.9266129321° = 160°55'34″ = 0.33329018445 rad
∠ B' = β' = 158.2622270269° = 158°15'44″ = 0.37993949557 rad
∠ C' = γ' = 40.81216004107° = 40°48'42″ = 2.42992958534 rad

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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 = 15 ; ; b = 17 ; ; c = 30 ; ;

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

p = a+b+c = 15+17+30 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-15)(31-17)(31-30) } ; ; T = sqrt{ 6944 } = 83.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.33 }{ 15 } = 11.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.33 }{ 17 } = 9.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.33 }{ 30 } = 5.56 ; ;

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{ 15**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 19° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 21° 44'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 139° 11'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.33 }{ 31 } = 2.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 19° 4'26" } = 22.95 ; ;




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