1. The problem involves three topics: Trigonometry, Indices, and Quadratics. 2. Let's start with Trigonometry: calculating angles using the tangent function, which relates the angle of elevation to the gradient. 3. The formula for tangent is $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ where $\theta$ is the angle. 4. For Indices, when bases are different, express numbers with the same base if possible or use logarithms to solve equations. 5. Scientific notation expresses numbers as $$a \times 10^n$$ where $1 \leq a < 10$ and $n$ is an integer. 6. For Quadratics, the Highest Common Factor (HCF) helps factorize expressions. 7. The Null Factor Law states if $$ab=0$$ then $$a=0$$ or $$b=0$$. 8. The Discriminant of a quadratic equation $$ax^2 + bx + c = 0$$ is $$D = b^2 - 4ac$$. 9. The roots are found using the formula $$x = \frac{-b \pm \sqrt{D}}{2a}$$. This overview covers the key formulas and rules for the topics mentioned.