Mathematics: Class 10 — Chapter 9: Some Applications of Trigonometry

• Line of Sight: The line drawn from the eye of an observer to the point in the object viewed by the observer.
• Angle of Elevation: The angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level (i.e., when raising one's head to look up).
• Angle of Depression: The angle formed by the line of sight with the horizontal when the point being viewed is below the horizontal level (i.e., when lowering one's head to look down).

To determine heights or distances without direct measurement, physical scenarios are modeled as right-angled triangles:

• Tangent (tan θ): Used when dealing with the opposite side (height) and adjacent side (distance). Formula: tan θ = Opposite / Adjacent.
• Sine (sin θ): Used when the hypotenuse (e.g., length of a ladder or rope) is involved. Formula: sin θ = Opposite / Hypotenuse.
• Cosine (cos θ): Used when relating the adjacent side to the hypotenuse. Formula: cos θ = Adjacent / Hypotenuse.

• Single Right Triangle: Finding the height of a tower given the distance from its foot and the angle of elevation. (e.g., tan 60° = h / 15).
• Observer Height Included: Total height of an object is calculated as Height = Calculated Height (BC) + Observer's Height (AE).
• Double Right Triangles (Two Angles): Scenarios involving two different angles of elevation/depression (e.g., a flagstaff on top of a building, or a changing shadow length). These require setting up simultaneous equations using a shared side.