Right triangle calculator (a,b)

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 isosceles triangle.

Sides: a = 90   b = 90   c = 127.2799220614

Area: T = 4050
Perimeter: p = 307.2799220614
Semiperimeter: s = 153.6439610307

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 90
Height: hb = 90
Height: hc = 63.64396103068

Median: ma = 100.6233058988
Median: mb = 100.6233058988
Median: mc = 63.64396103068

Inradius: r = 26.36603896932
Circumradius: R = 63.64396103068

Vertex coordinates: A[127.2799220614; 0] B[0; 0] C[63.64396103068; 63.64396103068]
Centroid: CG[63.64396103068; 21.21332034356]
Coordinates of the circumscribed circle: U[63.64396103068; -0]
Coordinates of the inscribed circle: I[63.64396103068; 26.36603896932]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a cathetus b

a = 90 ; ; b = 90 ; ;

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{ 90**2 + 90**2 } = 127.279 ; ;


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 = 90 ; ; b = 90 ; ; c = 127.28 ; ;

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

p = a+b+c = 90+90+127.28 = 307.28 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 307.28 }{ 2 } = 153.64 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 153.64 * (153.64-90)(153.64-90)(153.64-127.28) } ; ; T = sqrt{ 16402500 } = 4050 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4050 }{ 90 } = 90 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4050 }{ 90 } = 90 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4050 }{ 127.28 } = 63.64 ; ;

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{ 90**2-90**2-127.28**2 }{ 2 * 90 * 127.28 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-90**2-127.28**2 }{ 2 * 90 * 127.28 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 127.28**2-90**2-90**2 }{ 2 * 90 * 90 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4050 }{ 153.64 } = 26.36 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 90 }{ 2 * sin 45° } = 63.64 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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