📚 Topic Summary
Right triangle trigonometry is all about using the relationships between angles and sides of right triangles to solve problems. When dealing with word problems, it's crucial to visualize the scenario, identify the right triangle, and determine which trigonometric ratio (sine, cosine, or tangent) relates the given information to what you're trying to find. Remember SOH CAH TOA! This handy acronym reminds us that $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.
Word problems often involve angles of elevation (the angle looking upwards) and angles of depression (the angle looking downwards). Drawing a diagram is always the first step toward success!
🧠 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Angle of Elevation |
A. The ratio of the opposite side to the hypotenuse. |
| 2. Angle of Depression |
B. The angle formed by a horizontal line and the line of sight looking upwards. |
| 3. Sine |
C. The ratio of the adjacent side to the hypotenuse. |
| 4. Cosine |
D. The angle formed by a horizontal line and the line of sight looking downwards. |
| 5. Tangent |
E. The ratio of the opposite side to the adjacent side. |
✍️ Part B: Fill in the Blanks
Trigonometry involves the study of the relationship between ______ and sides of ______ . The three basic trigonometric ratios are ______, cosine, and ______. When solving word problems, it's important to ______ the situation and identify the relevant ______. Remember SOH CAH TOA, where SOH stands for Opposite over ______, CAH stands for Adjacent over ______, and TOA stands for Opposite over ______.
🤔 Part C: Critical Thinking
Explain, in your own words, how you can use trigonometry to find the height of a tree without climbing it. What measurements would you need to take, and how would you use trigonometric ratios to calculate the height?