Right triangle calculator (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 cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 193.649916731   b = 50   c = 200

Area: T = 4841.229918276
Perimeter: p = 443.649916731
Semiperimeter: s = 221.8254583655

Angle ∠ A = α = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ B = β = 14.47875121859° = 14°28'39″ = 0.25326802551 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 50
Height: hb = 193.649916731
Height: hc = 48.41222918276

Median: ma = 108.9722473588
Median: mb = 195.2566241898
Median: mc = 100

Inradius: r = 21.82545836552
Circumradius: R = 100

Vertex coordinates: A[200; 0] B[0; 0] C[187.5; 48.41222918276]
Centroid: CG[129.1676666667; 16.13774306092]
Coordinates of the circumscribed circle: U[100; -0]
Coordinates of the inscribed circle: I[171.8254583655; 21.82545836552]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ B' = β' = 165.5222487814° = 165°31'21″ = 0.25326802551 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b hypotenuse c

b = 50 ; ; c = 200 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 200**2 - 50**2 } = 193.649 ; ;


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 = 193.65 ; ; b = 50 ; ; c = 200 ; ;

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

p = a+b+c = 193.65+50+200 = 443.65 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 443.65 }{ 2 } = 221.82 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 221.82 * (221.82-193.65)(221.82-50)(221.82-200) } ; ; T = sqrt{ 23437500 } = 4841.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4841.23 }{ 193.65 } = 50 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4841.23 }{ 50 } = 193.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4841.23 }{ 200 } = 48.41 ; ;

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{ 193.65**2-50**2-200**2 }{ 2 * 50 * 200 } ) = 75° 31'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50**2-193.65**2-200**2 }{ 2 * 193.65 * 200 } ) = 14° 28'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 200**2-193.65**2-50**2 }{ 2 * 50 * 193.65 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4841.23 }{ 221.82 } = 21.82 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 193.65 }{ 2 * sin 75° 31'21" } = 100 ; ;
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