7 17 18 triangle

Acute scalene triangle.

Sides: a = 7   b = 17   c = 18

Area: T = 59.39769696197
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 22.84435073179° = 22°50'37″ = 0.39986944154 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 86.62877133166° = 86°37'40″ = 1.51219388208 rad

Height: ha = 16.97105627485
Height: hb = 6.98878787788
Height: hc = 6.65996632911

Median: ma = 17.15437167984
Median: mb = 10.68987791632
Median: mc = 9.38108315196

Inradius: r = 2.82884271247
Circumradius: R = 9.01656114601

Vertex coordinates: A[18; 0] B[0; 0] C[2.33333333333; 6.65996632911]
Centroid: CG[6.77877777778; 2.21998877637]
Coordinates of the circumscribed circle: U[9; 0.53303300859]
Coordinates of the inscribed circle: I[4; 2.82884271247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.1566492682° = 157°9'23″ = 0.39986944154 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 93.37222866834° = 93°22'20″ = 1.51219388208 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 = 17 ; ; c = 18 ; ;

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

p = a+b+c = 7+17+18 = 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)(21-17)(21-18) } ; ; T = sqrt{ 3528 } = 59.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.4 }{ 7 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.4 }{ 17 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.4 }{ 18 } = 6.6 ; ;

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**2-18**2 }{ 2 * 17 * 18 } ) = 22° 50'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-18**2 }{ 2 * 7 * 18 } ) = 70° 31'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 86° 37'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.4 }{ 21 } = 2.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 22° 50'37" } = 9.02 ; ;




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