Right triangle calculator (c,v)

Please enter two properties of the right triangle

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


You have entered hypotenuse c and height h.

Right scalene triangle.

Sides: a = 173.0666461222   b = 115.3787640815   c = 208

Area: T = 9984
Perimeter: p = 496.4444102037
Semiperimeter: s = 248.2222051019

Angle ∠ A = α = 56.3109932474° = 56°18'36″ = 0.98327937232 rad
Angle ∠ B = β = 33.6990067526° = 33°41'24″ = 0.58880026035 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 115.3787640815
Height: hb = 173.0666461222
Height: hc = 96

Median: ma = 144.2222051019
Median: mb = 182.4288068016
Median: mc = 104

Inradius: r = 40.22220510186
Circumradius: R = 104

Vertex coordinates: A[208; 0] B[0; 0] C[144; 96]
Centroid: CG[117.3333333333; 32]
Coordinates of the circumscribed circle: U[104; 0]
Coordinates of the inscribed circle: I[132.8444410204; 40.22220510186]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.6990067526° = 123°41'24″ = 0.98327937232 rad
∠ B' = β' = 146.3109932474° = 146°18'36″ = 0.58880026035 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c height h

c = 208 ; ; hc = 96 ; ;

2. From hypotenuse c and we calculate a,b - Pythagorean theorem, Euclid's theorem:

c = c_1+c_2 ; ; h**2 = c_1 * c_2 ; ; ; ; h**2 = c_1 * (c-c_1) ; ; h**2 = c_1 * c-c_1 **2 ; ; ; ; c_1**2 -c_1 * c + h**2 = 0 ; ; ; ; c_1**2 -208 * c_1 + 9216 = 0 ; ; ; ; c_1 = 144 ; ; c_2 = 64 ; ; ; ; a = sqrt{ c_1**2+h**2 } = sqrt{ 144**2+96**2 } = 173.066 ; ; b = sqrt{ c_2**2+h**2 } = sqrt{ 64**2+96**2 } = 115.378 ; ;


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 = 173.07 ; ; b = 115.38 ; ; c = 208 ; ;

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

p = a+b+c = 173.07+115.38+208 = 496.44 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 496.44 }{ 2 } = 248.22 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 248.22 * (248.22-173.07)(248.22-115.38)(248.22-208) } ; ; T = sqrt{ 99680256 } = 9984 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9984 }{ 173.07 } = 115.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9984 }{ 115.38 } = 173.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9984 }{ 208 } = 96 ; ;

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{ 173.07**2-115.38**2-208**2 }{ 2 * 115.38 * 208 } ) = 56° 18'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 115.38**2-173.07**2-208**2 }{ 2 * 173.07 * 208 } ) = 33° 41'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 208**2-173.07**2-115.38**2 }{ 2 * 115.38 * 173.07 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9984 }{ 248.22 } = 40.22 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 173.07 }{ 2 * sin 56° 18'36" } = 104 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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