9 20 25 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 20   c = 25

Area: T = 82.48663625092
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 19.26554645654° = 19°15'56″ = 0.33662457886 rad
Angle ∠ B = β = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ C = γ = 113.5788178478° = 113°34'41″ = 1.98223131729 rad

Height: ha = 18.33303027798
Height: hb = 8.24986362509
Height: hc = 6.59989090007

Median: ma = 22.18767077323
Median: mb = 15.90659737206
Median: mc = 9.17987798753

Inradius: r = 3.05550504633
Circumradius: R = 13.63986181397

Vertex coordinates: A[25; 0] B[0; 0] C[6.12; 6.59989090007]
Centroid: CG[10.37333333333; 2.21996363336]
Coordinates of the circumscribed circle: U[12.5; -5.45554472559]
Coordinates of the inscribed circle: I[7; 3.05550504633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.7354535435° = 160°44'4″ = 0.33662457886 rad
∠ B' = β' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ C' = γ' = 66.42218215218° = 66°25'19″ = 1.98223131729 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 = 9 ; ; b = 20 ; ; c = 25 ; ;

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

p = a+b+c = 9+20+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-9)(27-20)(27-25) } ; ; T = sqrt{ 6804 } = 82.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.49 }{ 9 } = 18.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.49 }{ 20 } = 8.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.49 }{ 25 } = 6.6 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 19° 15'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-9**2-25**2 }{ 2 * 9 * 25 } ) = 47° 9'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-9**2-20**2 }{ 2 * 20 * 9 } ) = 113° 34'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.49 }{ 27 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 15'56" } = 13.64 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.