# Right triangle calculator (B,a,h)

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, height h and angle β.

### Right scalene triangle.

Sides: a = 41   b = 67.2200031981   c = 78.72200374634

Area: T = 1377.601065561
Perimeter: p = 186.9220069444
Semiperimeter: s = 93.46600347222

Angle ∠ A = α = 31.38881498279° = 31°23'17″ = 0.54878265606 rad
Angle ∠ B = β = 58.61218501721° = 58°36'43″ = 1.02329697662 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 67.2200031981
Height: hb = 41
Height: hc = 35

Median: ma = 70.25773433759
Median: mb = 53.00990659658
Median: mc = 39.36600187317

Inradius: r = 14.74399972588
Circumradius: R = 39.36600187317

Vertex coordinates: A[78.72200374634; 0] B[0; 0] C[21.35441565041; 35]
Centroid: CG[33.35880646558; 11.66766666667]
Coordinates of the circumscribed circle: U[39.36600187317; 0]
Coordinates of the inscribed circle: I[26.26600027412; 14.74399972588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.6121850172° = 148°36'43″ = 0.54878265606 rad
∠ B' = β' = 121.3888149828° = 121°23'17″ = 1.02329697662 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: cathetus a, angle β and height h ### 2. From angle β we calculate angle α: ### 3. From height h and cathetus a we calculate hypotenuse c - Euclid's theorem: ### 4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem: 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area - from two legs ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle - basic use of sine function ### 10. Inradius ### 11. Circumradius ### 12. Calculation of medians 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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