AMA1D01C by Dr. Joseph Lee : The Spherical Sine Law
In spherical trigonometry, the law of sines connects the inner angles ($A, B, C$) of a spherical triangle to the angular lengths of its opposite great-circle sides ($a, b, c$).
The law states: $\frac{\sin a}{\sin A} = \frac{\sin b}{\sin B} = \frac{\sin c}{\sin C}$
Drag the canvas to rotate the sphere. Use the sliders below to move points A, B, and C and watch the ratios dynamically equalize.
Point A
Point B
Point C
| Pair (Vertex & Opposite Side) | Angle / Side (Degrees) | Sine Value | Ratio ($\frac{\sin(\text{side})}{\sin(\text{Angle})}$) |
|---|---|---|---|
| Angle A Side a |
$A =$ 0° $a =$ 0° |
$\sin(A) =$ 0 $\sin(a) =$ 0 |
0 |
| Angle B Side b |
$B =$ 0° $b =$ 0° |
$\sin(B) =$ 0 $\sin(b) =$ 0 |
0 |
| Angle C Side c |
$C =$ 0° $c =$ 0° |
$\sin(C) =$ 0 $\sin(c) =$ 0 |
0 |
Ratio = Constant