7 16 17 triangle

Acute scalene triangle.

Sides: a = 7   b = 16   c = 17

Area: T = 55.85769601751
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 24.25496286025° = 24°14'59″ = 0.42332358615 rad
Angle ∠ B = β = 69.84664151556° = 69°50'47″ = 1.21990499152 rad
Angle ∠ C = γ = 85.90439562418° = 85°54'14″ = 1.49993068769 rad

Height: ha = 15.95991314786
Height: hb = 6.98221200219
Height: hc = 6.57114070794

Median: ma = 16.13222658049
Median: mb = 10.2476950766
Median: mc = 8.95882364336

Inradius: r = 2.79328480088
Circumradius: R = 8.52217670011

Vertex coordinates: A[17; 0] B[0; 0] C[2.41217647059; 6.57114070794]
Centroid: CG[6.47105882353; 2.19904690265]
Coordinates of the circumscribed circle: U[8.5; 0.60986976429]
Coordinates of the inscribed circle: I[4; 2.79328480088]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.7550371397° = 155°45'1″ = 0.42332358615 rad
∠ B' = β' = 110.1543584844° = 110°9'13″ = 1.21990499152 rad
∠ C' = γ' = 94.09660437582° = 94°5'46″ = 1.49993068769 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 = 16 ; ; c = 17 ; ;

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

p = a+b+c = 7+16+17 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-7)(20-16)(20-17) } ; ; T = sqrt{ 3120 } = 55.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.86 }{ 7 } = 15.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.86 }{ 16 } = 6.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.86 }{ 17 } = 6.57 ; ;

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**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 24° 14'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-7**2-17**2 }{ 2 * 7 * 17 } ) = 69° 50'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-7**2-16**2 }{ 2 * 16 * 7 } ) = 85° 54'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.86 }{ 20 } = 2.79 ; ;

7. Circumradius

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




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