9 25 25 triangle

Acute isosceles triangle.

Sides: a = 9   b = 25   c = 25

Area: T = 110.6622493646
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 20.7439519611° = 20°44'22″ = 0.36219729025 rad
Angle ∠ B = β = 79.63302401945° = 79°37'49″ = 1.39898098755 rad
Angle ∠ C = γ = 79.63302401945° = 79°37'49″ = 1.39898098755 rad

Height: ha = 24.59216652547
Height: hb = 8.85329994917
Height: hc = 8.85329994917

Median: ma = 24.59216652547
Median: mb = 14.02767601391
Median: mc = 14.02767601391

Inradius: r = 3.75112709711
Circumradius: R = 12.708755749

Vertex coordinates: A[25; 0] B[0; 0] C[1.62; 8.85329994917]
Centroid: CG[8.87333333333; 2.95109998306]
Coordinates of the circumscribed circle: U[12.5; 2.28773603482]
Coordinates of the inscribed circle: I[4.5; 3.75112709711]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.2660480389° = 159°15'38″ = 0.36219729025 rad
∠ B' = β' = 100.3769759805° = 100°22'11″ = 1.39898098755 rad
∠ C' = γ' = 100.3769759805° = 100°22'11″ = 1.39898098755 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 = 9 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 9+25+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-9)(29.5-25)(29.5-25) } ; ; T = sqrt{ 12246.19 } = 110.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 110.66 }{ 9 } = 24.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 110.66 }{ 25 } = 8.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 110.66 }{ 25 } = 8.85 ; ;

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{ 9**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 20° 44'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 79° 37'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-25**2 }{ 2 * 25 * 9 } ) = 79° 37'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 110.66 }{ 29.5 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 20° 44'22" } = 12.71 ; ;




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