7 17 20 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 17   c = 20

Area: T = 57.44656264654
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 19.75499227956° = 19°45' = 0.34547011798 rad
Angle ∠ B = β = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ C = γ = 105.1099981783° = 105°6' = 1.83443407259 rad

Height: ha = 16.4133036133
Height: hb = 6.75883089959
Height: hc = 5.74545626465

Median: ma = 18.22877261336
Median: mb = 12.33989626793
Median: mc = 8.30766238629

Inradius: r = 2.61111648393
Circumradius: R = 10.35876205294

Vertex coordinates: A[20; 0] B[0; 0] C[4; 5.74545626465]
Centroid: CG[8; 1.91548542155]
Coordinates of the circumscribed circle: U[10; -2.69882036673]
Coordinates of the inscribed circle: I[5; 2.61111648393]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.2550077204° = 160°15' = 0.34547011798 rad
∠ B' = β' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ C' = γ' = 74.99000182166° = 74°54' = 1.83443407259 rad

Calculate another triangle




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 = 17 ; ; c = 20 ; ;

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

p = a+b+c = 7+17+20 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-7)(22-17)(22-20) } ; ; T = sqrt{ 3300 } = 57.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.45 }{ 7 } = 16.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.45 }{ 17 } = 6.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.45 }{ 20 } = 5.74 ; ;

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**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 19° 45' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 55° 9' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 105° 6' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.45 }{ 22 } = 2.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 19° 45' } = 10.36 ; ;




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