4 22 25 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 22   c = 25

Area: T = 30.97547881349
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 6.46772683912° = 6°28'2″ = 0.1132875127 rad
Angle ∠ B = β = 38.27993217379° = 38°16'46″ = 0.66881001998 rad
Angle ∠ C = γ = 135.2533409871° = 135°15'12″ = 2.36106173268 rad

Height: ha = 15.48773940674
Height: hb = 2.81658898304
Height: hc = 2.47879830508

Median: ma = 23.46327364133
Median: mb = 14.12444468918
Median: mc = 9.68224583655

Inradius: r = 1.21546975739
Circumradius: R = 17.75663764958

Vertex coordinates: A[25; 0] B[0; 0] C[3.14; 2.47879830508]
Centroid: CG[9.38; 0.82659943503]
Coordinates of the circumscribed circle: U[12.5; -12.61110628521]
Coordinates of the inscribed circle: I[3.5; 1.21546975739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.5332731609° = 173°31'58″ = 0.1132875127 rad
∠ B' = β' = 141.7210678262° = 141°43'14″ = 0.66881001998 rad
∠ C' = γ' = 44.74765901291° = 44°44'48″ = 2.36106173268 rad

Calculate another triangle




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 = 4 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 4+22+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-4)(25.5-22)(25.5-25) } ; ; T = sqrt{ 959.44 } = 30.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.97 }{ 4 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.97 }{ 22 } = 2.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.97 }{ 25 } = 2.48 ; ;

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{ 4**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 6° 28'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-4**2-25**2 }{ 2 * 4 * 25 } ) = 38° 16'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-4**2-22**2 }{ 2 * 22 * 4 } ) = 135° 15'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.97 }{ 25.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 6° 28'2" } = 17.76 ; ;




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