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 = 150   b = 150   c = 212.1322034356

Area: T = 11250
Perimeter: p = 512.1322034356
Semiperimeter: s = 256.0666017178

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

Height: ha = 150
Height: hb = 150
Height: hc = 106.0666017178

Median: ma = 167.7055098313
Median: mb = 167.7055098313
Median: mc = 106.0666017178

Inradius: r = 43.9343982822
Circumradius: R = 106.0666017178

Vertex coordinates: A[212.1322034356; 0] B[0; 0] C[106.0666017178; 106.0666017178]
Centroid: CG[106.0666017178; 35.35553390593]
Coordinates of the circumscribed circle: U[106.0666017178; 0]
Coordinates of the inscribed circle: I[106.0666017178; 43.9343982822]

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 and cathetus b

a = 150 ; ; b = 150 ; ;

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{ 150**2 + 150**2 } = 212.132 ; ;
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 = 150 ; ; b = 150 ; ; c = 212.13 ; ;

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

p = a+b+c = 150+150+212.13 = 512.13 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 512.13 }{ 2 } = 256.07 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 150 * 150 }{ 2 } = 11250 ; ;

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

h _a = b = 150 ; ; h _b = a = 150 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11250 }{ 212.13 } = 106.07 ; ;

7. Calculation of the inner angles of the triangle - basic use of sine function

sin alpha = fraction{ a }{ c } ; ; alpha = arcsin( fraction{ a }{ c } ) = arcsin( fraction{ 150 }{ 212.13 } ) = 45° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 150 }{ 212.13 } ) = 45° ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11250 }{ 256.07 } = 43.93 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 150 }{ 2 * sin 45° } = 106.07 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 150**2+2 * 212.13**2 - 150**2 } }{ 2 } = 167.705 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 212.13**2+2 * 150**2 - 150**2 } }{ 2 } = 167.705 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 150**2+2 * 150**2 - 212.13**2 } }{ 2 } = 106.066 ; ;
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Trigonometry right triangle solver. You can calculate angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height. A right-angled triangle is entirely determined by two independent properties. Step-by-step explanations are provided for each calculation.

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