NapkinCalc

Trigonometry

Any triangle: law of sines

continues from lesson 4 — values defined earlier in the course stay live here

The law of sines relates each side to the angle opposite it: sin(A)/a = sin(B)/b. Given one matched side-angle pair and one more side, the opposite angle follows.

sided=8side_{d} = 8 known side
angD:=60degang_{D} := 60 deg = 60 deg angle opposite it
sidee=6side_{e} = 6 second known side
angE=asin(sidee⋅sin(angD)sided)ang_{E} = \mathrm{asin}\left(\frac{side_{e} \cdot \mathrm{sin}\left(ang_{D}\right)}{side_{d}}\right) = 0.70700.7070 angle opposite side_e

Where next: plot tan(x) and find its vertical asymptotes, or use the Σ Formulas library to insert the arc-length and sector formulas and connect angles to distances along the circle.