17 26 30 triangle

Acute scalene triangle.

Sides: a = 17   b = 26   c = 30

Area: T = 220.4021763831
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 34.41215086698° = 34°24'41″ = 0.60105941269 rad
Angle ∠ B = β = 59.80552218091° = 59°48'19″ = 1.04437980305 rad
Angle ∠ C = γ = 85.78332695211° = 85°47' = 1.49772004963 rad

Height: ha = 25.93296192743
Height: hb = 16.95439818332
Height: hc = 14.69334509221

Median: ma = 26.75435044433
Median: mb = 20.62876513447
Median: mc = 16.04768065359

Inradius: r = 6.03884044885
Circumradius: R = 15.04107144769

Vertex coordinates: A[30; 0] B[0; 0] C[8.55; 14.69334509221]
Centroid: CG[12.85; 4.8987816974]
Coordinates of the circumscribed circle: U[15; 1.1065934888]
Coordinates of the inscribed circle: I[10.5; 6.03884044885]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.588849133° = 145°35'19″ = 0.60105941269 rad
∠ B' = β' = 120.1954778191° = 120°11'41″ = 1.04437980305 rad
∠ C' = γ' = 94.21767304789° = 94°13' = 1.49772004963 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 = 17 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 17+26+30 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-17)(36.5-26)(36.5-30) } ; ; T = sqrt{ 48576.94 } = 220.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 220.4 }{ 17 } = 25.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 220.4 }{ 26 } = 16.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 220.4 }{ 30 } = 14.69 ; ;

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{ 17**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 34° 24'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 59° 48'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-26**2 }{ 2 * 26 * 17 } ) = 85° 47' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 220.4 }{ 36.5 } = 6.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 24'41" } = 15.04 ; ;




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