3 15 17 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 15   c = 17

Area: T = 17.8109758561
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 8.03295831464° = 8°1'46″ = 0.14401426635 rad
Angle ∠ B = β = 44.30105298893° = 44°18'2″ = 0.77331901069 rad
Angle ∠ C = γ = 127.6769886964° = 127°40'12″ = 2.22882598832 rad

Height: ha = 11.8733172374
Height: hb = 2.37546344748
Height: hc = 2.09552657131

Median: ma = 15.96108896995
Median: mb = 9.63106801421
Median: mc = 6.69895440801

Inradius: r = 1.01877004892
Circumradius: R = 10.73884948171

Vertex coordinates: A[17; 0] B[0; 0] C[2.14770588235; 2.09552657131]
Centroid: CG[6.38223529412; 0.69884219044]
Coordinates of the circumscribed circle: U[8.5; -6.56224134993]
Coordinates of the inscribed circle: I[2.5; 1.01877004892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.9770416854° = 171°58'14″ = 0.14401426635 rad
∠ B' = β' = 135.6999470111° = 135°41'58″ = 0.77331901069 rad
∠ C' = γ' = 52.33301130357° = 52°19'48″ = 2.22882598832 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 = 3 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 3+15+17 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-3)(17.5-15)(17.5-17) } ; ; T = sqrt{ 317.19 } = 17.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.81 }{ 3 } = 11.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.81 }{ 15 } = 2.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.81 }{ 17 } = 2.1 ; ;

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{ 3**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 8° 1'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-3**2-17**2 }{ 2 * 3 * 17 } ) = 44° 18'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-3**2-15**2 }{ 2 * 15 * 3 } ) = 127° 40'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.81 }{ 17.5 } = 1.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 8° 1'46" } = 10.74 ; ;




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