Right triangle calculator (a,b,c)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 3.6   b = 9.8   c = 10.2

Area: T = 17.59663632606
Perimeter: p = 23.6
Semiperimeter: s = 11.8

Angle ∠ A = α = 20.61438611676° = 20°36'50″ = 0.36597797489 rad
Angle ∠ B = β = 73.41770576716° = 73°25'1″ = 1.28113693835 rad
Angle ∠ C = γ = 85.96990811608° = 85°58'9″ = 1.55004435212 rad

Height: ha = 9.7765757367
Height: hb = 3.5911094543
Height: hc = 3.4550267306

Median: ma = 9.8398699101
Median: mb = 5.8732818744
Median: mc = 5.3387602458

Inradius: r = 1.49112172255
Circumradius: R = 5.11326473503

Vertex coordinates: A[10.2; 0] B[0; 0] C[1.02774509804; 3.4550267306]
Centroid: CG[3.74224836601; 1.1550089102]
Coordinates of the circumscribed circle: U[5.1; 0.35993924441]
Coordinates of the inscribed circle: I[2; 1.49112172255]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.3866138832° = 159°23'10″ = 0.36597797489 rad
∠ B' = β' = 106.5832942328° = 106°34'59″ = 1.28113693835 rad
∠ C' = γ' = 94.03109188392° = 94°1'51″ = 1.55004435212 rad

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How did we calculate this triangle?

1. Input data entered: side a b c

a = 3.6 ; ; b = 9.8 ; ; c = 10.2 ; ;


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 = 3.6 ; ; b = 9.8 ; ; c = 10.2 ; ; : Nr. 1

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

p = a+b+c = 3.6+9.8+10.2 = 23.6 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.6 }{ 2 } = 11.8 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.8 * (11.8-3.6)(11.8-9.8)(11.8-10.2) } ; ; T = sqrt{ 309.63 } = 17.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.6 }{ 3.6 } = 9.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.6 }{ 9.8 } = 3.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.6 }{ 10.2 } = 3.45 ; ;

6. 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{ 3.6**2-9.8**2-10.2**2 }{ 2 * 9.8 * 10.2 } ) = 20° 36'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.8**2-3.6**2-10.2**2 }{ 2 * 3.6 * 10.2 } ) = 73° 25'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.2**2-3.6**2-9.8**2 }{ 2 * 9.8 * 3.6 } ) = 85° 58'9" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.6 }{ 11.8 } = 1.49 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.6 }{ 2 * sin 20° 36'50" } = 5.11 ; ;
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