NapkinCalc

Trigonometry

Right triangles — SOH CAH TOA

In a right triangle, the three sides are related by the Pythagorean theorem, and each acute angle is pinned down by the RATIO of two sides: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

lega=3leg_{a} = 3 adjacent leg
legb=4leg_{b} = 4 opposite leg
hypc=lega2+legb2hyp_{c} = \sqrt{leg_{a}^{2} + leg_{b}^{2}} = 55 Pythagorean theorem
θ=atan(legblega)\theta = \mathrm{atan}\left(\frac{leg_{b}}{leg_{a}}\right) = 0.92730.9273 angle from the tangent ratio
θdeg=θ⋅180π\theta_{deg} = \frac{\theta \cdot 180}{\pi} = 53.130153.1301 the same angle in degrees

right(leg_a, leg_b)

34553.13°A90°B36.87°C

drawn to scale — note the right-angle mark

Try it: set leg_a and leg_b equal. The angle becomes 45° and the triangle becomes the isosceles right triangle. The drawing follows.