14 17 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 30

Area: T = 58.28332523114
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 13.2122412139° = 13°12'45″ = 0.2310600094 rad
Angle ∠ B = β = 16.11333969958° = 16°6'48″ = 0.28112318313 rad
Angle ∠ C = γ = 150.6744190865° = 150°40'27″ = 2.63297607284 rad

Height: ha = 8.32661789016
Height: hb = 6.85768532131
Height: hc = 3.88655501541

Median: ma = 23.35659414283
Median: mb = 21.81216941112
Median: mc = 4.18333001327

Inradius: r = 1.91109263053
Circumradius: R = 30.62662936471

Vertex coordinates: A[30; 0] B[0; 0] C[13.45; 3.88655501541]
Centroid: CG[14.48333333333; 1.29551833847]
Coordinates of the circumscribed circle: U[15; -26.70114955117]
Coordinates of the inscribed circle: I[13.5; 1.91109263053]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.7887587861° = 166°47'15″ = 0.2310600094 rad
∠ B' = β' = 163.8876603004° = 163°53'12″ = 0.28112318313 rad
∠ C' = γ' = 29.32658091348° = 29°19'33″ = 2.63297607284 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 = 14 ; ; b = 17 ; ; c = 30 ; ;

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

p = a+b+c = 14+17+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-14)(30.5-17)(30.5-30) } ; ; T = sqrt{ 3396.94 } = 58.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.28 }{ 14 } = 8.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.28 }{ 17 } = 6.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.28 }{ 30 } = 3.89 ; ;

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{ 14**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 13° 12'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 16° 6'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 150° 40'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.28 }{ 30.5 } = 1.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 13° 12'45" } = 30.63 ; ;




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