Right triangle calculator (a,b) - result

Please enter two properties of the right triangle

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


You have entered cathetus a and cathetus b.

Right scalene triangle.

Sides: a = 15   b = 8   c = 17

Area: T = 60
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 61.92875130641° = 61°55'39″ = 1.08108390005 rad
Angle ∠ B = β = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 8
Height: hb = 15
Height: hc = 7.05988235294

Median: ma = 10.96658560997
Median: mb = 15.52441746963
Median: mc = 8.5

Inradius: r = 3
Circumradius: R = 8.5

Vertex coordinates: A[17; 0] B[0; 0] C[13.23552941176; 7.05988235294]
Centroid: CG[10.07884313725; 2.35329411765]
Coordinates of the circumscribed circle: U[8.5; -0]
Coordinates of the inscribed circle: I[12; 3]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.0722486936° = 118°4'21″ = 1.08108390005 rad
∠ B' = β' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a and cathetus b

a = 15 ; ; b = 8 ; ;

2. From cathetus a and cathetus b we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 15**2 + 8**2 } = 17 ; ;


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 = 15 ; ; b = 8 ; ; c = 17 ; ;

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

p = a+b+c = 15+8+17 = 40 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-15)(20-8)(20-17) } ; ; T = sqrt{ 3600 } = 60 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 60 }{ 15 } = 8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 60 }{ 8 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 60 }{ 17 } = 7.06 ; ;

7. 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{ 15**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 61° 55'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 28° 4'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-15**2-8**2 }{ 2 * 8 * 15 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 60 }{ 20 } = 3 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 61° 55'39" } = 8.5 ; ;
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