15 24 26 triangle

Acute scalene triangle.

Sides: a = 15   b = 24   c = 26

Area: T = 177.2676571863
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ B = β = 65.37656816478° = 65°22'32″ = 1.14110208955 rad
Angle ∠ C = γ = 80.00221565124° = 80°8″ = 1.39663010398 rad

Height: ha = 23.6365542915
Height: hb = 14.77222143219
Height: hc = 13.63658901433

Median: ma = 23.86994365246
Median: mb = 17.50771414
Median: mc = 15.21551240547

Inradius: r = 5.45443560573
Circumradius: R = 13.22004583572

Vertex coordinates: A[26; 0] B[0; 0] C[6.25; 13.63658901433]
Centroid: CG[10.75; 4.54552967144]
Coordinates of the circumscribed circle: U[13; 2.29217462426]
Coordinates of the inscribed circle: I[8.5; 5.45443560573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ B' = β' = 114.6244318352° = 114°37'28″ = 1.14110208955 rad
∠ C' = γ' = 99.99878434876° = 99°59'52″ = 1.39663010398 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 = 15 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 15+24+26 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-15)(32.5-24)(32.5-26) } ; ; T = sqrt{ 31423.44 } = 177.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 177.27 }{ 15 } = 23.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 177.27 }{ 24 } = 14.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 177.27 }{ 26 } = 13.64 ; ;

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{ 15**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 34° 37'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 65° 22'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-24**2 }{ 2 * 24 * 15 } ) = 80° 8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 177.27 }{ 32.5 } = 5.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 37'20" } = 13.2 ; ;




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