# **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. --- --- # **Key Concepts** This exercise focuses on the following concepts: * **Right-Angled Trigonometry:** Using SOH CAH TOA to solve for unknown sides and angles. * **Angles of Elevation and Depression:** Understanding the relationship between horizontal sightlines and objects above or below. * **Real-World Modeling:** Translating physical descriptions of ramps, roofs, and shadows into geometric diagrams. * **Inverse Trigonometric Functions:** Using $\sin^{-1}$, $\cos^{-1}$, and $\tan^{-1}$ to determine angles from side lengths. * **Proportional Reasoning:** Using similar triangles and shadows to determine heights. --- # **Important Formulas** Below are the key formulas used in this exercise: | Ratio | Formula | | :--- | :--- | | **Sine** | $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$ | | **Cosine** | $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$ | | **Tangent** | $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$ | | **Pythagorean Theorem** | $a^2 + b^2 = c^2$ | --- # **Summary** This exercise applies basic trigonometric principles to practical engineering, architecture, and surveying problems. The primary strategy involves identifying the right-angled triangle within a word problem, labeling the known components (angles or sides), and selecting the appropriate trigonometric ratio to solve for the unknown. Key learnings include the application of angles of elevation/depression and the use of inverse functions to find necessary construction pitches and slopes.