Aptitude Topics
Basic Concepts
The study of height and distance relies entirely on trigonometry within a right-angled triangle. By knowing one side (height or distance) and one angle, you can calculate the remaining dimensions.
Fundamental Principles
The SOH-CAH-TOA Mnemonic
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$.
Essential Formulation Tips
- Always draw a diagram first. Label the known angle, the known side, and the variable you need to solve for.
- Ensure your calculator is in 'Degree' mode before solving.
Example Breakdown: Finding a Simple Height
Problem QueryA ladder leans against a wall, making a 60° angle with the ground. If the ladder is 10m long, how high does it reach on the wall?
Step-By-Step Solution Path
We have the hypotenuse (10m) and the angle (60°). We need the opposite side (height).
Use Sine: $\sin(60^{\circ}) = \frac{\text{Height}}{10}$.
Height = $10 \times \sin(60^{\circ}) = 10 \times 0.866 = 8.66 \text{ meters}$.
No verification metrics evaluated yet.