gen-define-the-law-of-sines-and-give-one-short-worked-example-ee5d

Define the law of sines and give one short worked example.

# Law of Sines The **law of sines** states that for any triangle with sides *a*, *b*, *c* and opposite angles *A*, *B*, *C*: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ Equivalently: $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ ## Worked Example **Problem:** In triangle ABC, angle A = 30°, angle B = 45°, and side a = 10. Find side b. **Solution:** Using the law of sines: $$\frac{a}{\sin A} = \frac{b}{\sin B}$$ $$\frac{10}{\sin 30°} = \frac{b}{\sin 45°}$$ $$\frac{10}{0.5} = \frac{b}{0.707}$$ $$20 = \frac{b}{0.707}$$ $$b = 20 \times 0.707 = 14.14$$ Therefore, side *b* ≈ **14.14**