7 17 17 triangle

Acute isosceles triangle.

Sides: a = 7   b = 17   c = 17

Area: T = 58.22553166586
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 23.7622312042° = 23°45'44″ = 0.4154730583 rad
Angle ∠ B = β = 78.1198843979° = 78°7'8″ = 1.36334310353 rad
Angle ∠ C = γ = 78.1198843979° = 78°7'8″ = 1.36334310353 rad

Height: ha = 16.63658047596
Height: hb = 6.8550037254
Height: hc = 6.8550037254

Median: ma = 16.63658047596
Median: mb = 9.83661577865
Median: mc = 9.83661577865

Inradius: r = 2.84402593492
Circumradius: R = 8.68660841473

Vertex coordinates: A[17; 0] B[0; 0] C[1.44111764706; 6.8550037254]
Centroid: CG[6.14770588235; 2.28333457513]
Coordinates of the circumscribed circle: U[8.5; 1.78883114421]
Coordinates of the inscribed circle: I[3.5; 2.84402593492]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.2387687958° = 156°14'16″ = 0.4154730583 rad
∠ B' = β' = 101.8811156021° = 101°52'52″ = 1.36334310353 rad
∠ C' = γ' = 101.8811156021° = 101°52'52″ = 1.36334310353 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 = 17 ; ;

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

p = a+b+c = 7+17+17 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-7)(20.5-17)(20.5-17) } ; ; T = sqrt{ 3390.19 } = 58.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.23 }{ 7 } = 16.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.23 }{ 17 } = 6.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.23 }{ 17 } = 6.85 ; ;

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**2-17**2 }{ 2 * 17 * 17 } ) = 23° 45'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-17**2 }{ 2 * 7 * 17 } ) = 78° 7'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 78° 7'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.23 }{ 20.5 } = 2.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 23° 45'44" } = 8.69 ; ;




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