1. Statement of the problem: Compute $L_{eff} = \frac{30 \times 10^8}{2 \left(8 \times 10^9\right) \sqrt{2.015}}$ and find the area of the right triangle with vertices $(2,0)$, $(4,0)$, and $(4,8)$. 2. Formula used and important rules: we will directly substitute and simplify using arithmetic with powers of ten and a numerical square root. $$L_{eff} = \frac{30 \times 10^8}{2\left(8 \times 10^9\right)\sqrt{2.015}}$$ 3. Intermediate work — numerator: compute $30 \times 10^8 = 3.0\times10^9$. 4. Intermediate work — denominator factors: compute $2\left(8\times10^9\right) = 1.6\times10^{10}$. 5. Intermediate work — square root: evaluate $\sqrt{2.015} \approx 1.419636$. 6. Intermediate work — full denominator: multiply $1.6\times10^{10}\times1.419636 = 2.2714176\times10^{10}$. 7. Division to get $L_{eff}$: compute $$L_{eff} = \frac{3.0\times10^9}{2.2714176\times10^{10}} \approx 0.13208.$$ 8. Rounding: to four significant figures $L_{eff} \approx 0.1321$. 9. Triangle area — formula and rules: area of a right triangle is $\frac{1}{2}\times\text{base}\times\text{height}$. 10. Triangle dimensions: base from $(2,0)$ to $(4,0)$ has length $4-2=2$. 11. Triangle dimensions: height from $(4,0)$ to $(4,8)$ has length $8-0=8$. 12. Compute area: $$\text{Area} = \frac{1}{2}\times2\times8 = 8.$$ 13. Final answers: $L_{eff} \approx 0.13208$ (rounded $0.1321$) and triangle area $= 8$ square units.