Step-by-step explanation:
- The angle of elevation $\theta$ represents the angle between the line connecting two points and the horizontal direction. In other words, it measures how far up or down an object appears to be from your point of view. - A right triangle consists of three sides: opposite angles (OA), adjacent angles (AA), and hypotenuse (H). To solve this problem, we need to use basic trigonometric ratios like sine ($\sin2) Draw the two right triangles formed by the angles $alpha$ and $beta$. One triangle has its base on ground level, with height h. The other triangle has a hypotenuse of length d (distance between you and the chimney), with adjacent angle $\theta = beta - alpha$.
3) Use trigonometric ratios to find the unknown variables: sine ($sin$) for one triangle, cosine ($cos$) for another. By applying basic rules like inverse function theorem, we can derive an equation that relates these values to each other. For example: $h=d \cdot sin(90-alpha)$ where $h$ is the height of the chimney and $d$ is distance between you and it. Similarly, we can also use this method to calculate $\theta$, which represents elevation angle at your position relative to ground level when approaching! Hope this helps some how ✌
