7 15 17 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 15   c = 17

Area: T = 52.36659001641
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 24.25496286025° = 24°14'59″ = 0.42332358615 rad
Angle ∠ B = β = 61.65443276393° = 61°39'16″ = 1.07660710154 rad
Angle ∠ C = γ = 94.09660437582° = 94°5'46″ = 1.64222857767 rad

Height: ha = 14.96216857612
Height: hb = 6.98221200219
Height: hc = 6.1610694137

Median: ma = 15.64444878472
Median: mb = 10.61883802908
Median: mc = 8.04767384697

Inradius: r = 2.68554307776
Circumradius: R = 8.52217670011

Vertex coordinates: A[17; 0] B[0; 0] C[3.32435294118; 6.1610694137]
Centroid: CG[6.77545098039; 2.05435647123]
Coordinates of the circumscribed circle: U[8.5; -0.60986976429]
Coordinates of the inscribed circle: I[4.5; 2.68554307776]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.7550371397° = 155°45'1″ = 0.42332358615 rad
∠ B' = β' = 118.3465672361° = 118°20'44″ = 1.07660710154 rad
∠ C' = γ' = 85.90439562418° = 85°54'14″ = 1.64222857767 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 = 7 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 7+15+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-7)(19.5-15)(19.5-17) } ; ; T = sqrt{ 2742.19 } = 52.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.37 }{ 7 } = 14.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.37 }{ 15 } = 6.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.37 }{ 17 } = 6.16 ; ;

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{ 7**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 24° 14'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-17**2 }{ 2 * 7 * 17 } ) = 61° 39'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 94° 5'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.37 }{ 19.5 } = 2.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 24° 14'59" } = 8.52 ; ;




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