7 15 20 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 15   c = 20

Area: T = 42
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 16.26602047083° = 16°15'37″ = 0.28437941092 rad
Angle ∠ B = β = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ C = γ = 126.8769897646° = 126°52'12″ = 2.21442974356 rad

Height: ha = 12
Height: hb = 5.6
Height: hc = 4.2

Median: ma = 17.32877234512
Median: mb = 12.97111217711
Median: mc = 6.08327625303

Inradius: r = 2
Circumradius: R = 12.5

Vertex coordinates: A[20; 0] B[0; 0] C[5.6; 4.2]
Centroid: CG[8.53333333333; 1.4]
Coordinates of the circumscribed circle: U[10; -7.5]
Coordinates of the inscribed circle: I[6; 2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7439795292° = 163°44'23″ = 0.28437941092 rad
∠ B' = β' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ C' = γ' = 53.13301023542° = 53°7'48″ = 2.21442974356 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 = 20 ; ;

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

p = a+b+c = 7+15+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-7)(21-15)(21-20) } ; ; T = sqrt{ 1764 } = 42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42 }{ 7 } = 12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42 }{ 15 } = 5.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42 }{ 20 } = 4.2 ; ;

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**2-20**2 }{ 2 * 15 * 20 } ) = 16° 15'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 36° 52'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 126° 52'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42 }{ 21 } = 2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 15'37" } = 12.5 ; ;




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