7 20 24 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 24

Area: T = 62.38553949254
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 15.06664512874° = 15°3'59″ = 0.26329591816 rad
Angle ∠ B = β = 47.9660493671° = 47°57'38″ = 0.83770685254 rad
Angle ∠ C = γ = 116.9733055042° = 116°58'23″ = 2.04215649466 rad

Height: ha = 17.82443985501
Height: hb = 6.23985394925
Height: hc = 5.19987829105

Median: ma = 21.81216941112
Median: mb = 14.57773797371
Median: mc = 8.97221792225

Inradius: r = 2.44664860755
Circumradius: R = 13.46546899487

Vertex coordinates: A[24; 0] B[0; 0] C[4.68875; 5.19987829105]
Centroid: CG[9.56325; 1.73329276368]
Coordinates of the circumscribed circle: U[12; -6.10771986553]
Coordinates of the inscribed circle: I[5.5; 2.44664860755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.9343548713° = 164°56'1″ = 0.26329591816 rad
∠ B' = β' = 132.0439506329° = 132°2'22″ = 0.83770685254 rad
∠ C' = γ' = 63.02769449584° = 63°1'37″ = 2.04215649466 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 = 20 ; ; c = 24 ; ;

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

p = a+b+c = 7+20+24 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-7)(25.5-20)(25.5-24) } ; ; T = sqrt{ 3891.94 } = 62.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.39 }{ 7 } = 17.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.39 }{ 20 } = 6.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.39 }{ 24 } = 5.2 ; ;

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**2-20**2-24**2 }{ 2 * 20 * 24 } ) = 15° 3'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 47° 57'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 116° 58'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.39 }{ 25.5 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 3'59" } = 13.46 ; ;




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