Trigonometry B — Waves & the Triangle Laws

Any triangle: the law of sines

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: the law of sines says each side is proportional to the sine of the angle across from it: sin(A)/a = sin(B)/b. Know one matched side–angle pair plus one more side, and the opposite angle pops out.

side_{d} = 8

known side

ang_{D} := 60 deg

= 60 deg angle opposite it

side_{e} = 6

second known side

ang_{E} = \mathrm{asin}\left(\frac{side_{e} \cdot \mathrm{sin}\left(ang_{D}\right)}{side_{d}}\right)

0.7070

angle opposite side_e (radians)

✓ pass

\mathrm{sin}\left(ang_{E}\right) < \mathrm{sin}\left(ang_{D}\right)

the shorter side faces the smaller angle — a useful sanity check

Where next: Precalculus gathers every function — polynomial, rational, exponential — into one toolkit and points it at calculus.