97.5 163.25 190.149 triangle

Right scalene triangle.

Sides: a = 97.5   b = 163.25   c = 190.149

Area: T = 7958.437749989
Perimeter: p = 450.899
Semiperimeter: s = 225.45495

Angle ∠ A = α = 30.84875662492° = 30°50'51″ = 0.53883915973 rad
Angle ∠ B = β = 59.15327402624° = 59°9'10″ = 1.03224100792 rad
Angle ∠ C = γ = 909.9996934884° = 89°59'59″ = 1.57107909772 rad

Height: ha = 163.2549999998
Height: hb = 97.54999999986
Height: hc = 83.70773821044

Median: ma = 170.3733236896
Median: mb = 127.1576617899
Median: mc = 95.0754947803

Inradius: r = 35.33003111557
Circumradius: R = 95.07545000014

Vertex coordinates: A[190.149; 0] B[0; 0] C[49.99332413555; 83.70773821044]
Centroid: CG[80.04774137852; 27.90224607015]
Coordinates of the circumscribed circle: U[95.07545; 0.0010508614]
Coordinates of the inscribed circle: I[62.21995; 35.33003111557]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.1522433751° = 149°9'9″ = 0.53883915973 rad
∠ B' = β' = 120.8477259738° = 120°50'50″ = 1.03224100792 rad
∠ C' = γ' = 900.0003065116° = 90°1″ = 1.57107909772 rad

Calculate another triangle




How did we calculate this triangle?

a = 97.5 ; ; b = 163.25 ; ; c = 190.15 ; ;

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

p = a+b+c = 97.5+163.25+190.15 = 450.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 450.9 }{ 2 } = 225.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 225.45 * (225.45-97.5)(225.45-163.25)(225.45-190.15) } ; ; T = sqrt{ 63336727.44 } = 7958.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7958.44 }{ 97.5 } = 163.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7958.44 }{ 163.25 } = 97.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7958.44 }{ 190.15 } = 83.71 ; ;

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{ 97.5**2-163.25**2-190.15**2 }{ 2 * 163.25 * 190.15 } ) = 30° 50'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 163.25**2-97.5**2-190.15**2 }{ 2 * 97.5 * 190.15 } ) = 59° 9'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 190.15**2-97.5**2-163.25**2 }{ 2 * 163.25 * 97.5 } ) = 89° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7958.44 }{ 225.45 } = 35.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 97.5 }{ 2 * sin 30° 50'51" } = 95.07 ; ;




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

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