Right triangle calculator (a,c)

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 hypotenuse c.

Right scalene triangle.

Sides: a = 230   b = 131.6244465811   c = 265

Area: T = 15136.81435683
Perimeter: p = 626.6244465811
Semiperimeter: s = 313.3122232905

Angle ∠ A = α = 60.21883447657° = 60°13'6″ = 1.05110083863 rad
Angle ∠ B = β = 29.78216552343° = 29°46'54″ = 0.52197879405 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 131.6244465811
Height: hb = 230
Height: hc = 114.2440102402

Median: ma = 174.786558293
Median: mb = 239.2310537348
Median: mc = 132.5

Inradius: r = 48.31222329054
Circumradius: R = 132.5

Vertex coordinates: A[265; 0] B[0; 0] C[199.6232641509; 114.2440102402]
Centroid: CG[154.8744213836; 38.0880034134]
Coordinates of the circumscribed circle: U[132.5; 0]
Coordinates of the inscribed circle: I[181.6887767095; 48.31222329054]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 119.7821655234° = 119°46'54″ = 1.05110083863 rad
∠ B' = β' = 150.2188344766° = 150°13'6″ = 0.52197879405 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a hypotenuse c

a = 230 ; ; c = 265 ; ;

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

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 265**2 - 230**2 } = 131.624 ; ;


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 = 230 ; ; b = 131.62 ; ; c = 265 ; ;

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

p = a+b+c = 230+131.62+265 = 626.62 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 626.62 }{ 2 } = 313.31 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 313.31 * (313.31-230)(313.31-131.62)(313.31-265) } ; ; T = sqrt{ 229123125 } = 15136.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15136.81 }{ 230 } = 131.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15136.81 }{ 131.62 } = 230 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15136.81 }{ 265 } = 114.24 ; ;

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{ 230**2-131.62**2-265**2 }{ 2 * 131.62 * 265 } ) = 60° 13'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 131.62**2-230**2-265**2 }{ 2 * 230 * 265 } ) = 29° 46'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 265**2-230**2-131.62**2 }{ 2 * 131.62 * 230 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15136.81 }{ 313.31 } = 48.31 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 230 }{ 2 * sin 60° 13'6" } = 132.5 ; ;
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