Q1. In a two-position problem, what quantity remains constant?
✔ The height of the tower or building does not change even if the observer moves.
Q2. If you move closer to a tower, what happens to the angle of elevation?
✔ As distance decreases, the line of sight becomes steeper, increasing the angle.
Q3. Which trigonometric ratio relates height and base distance?
✔ Tangent is defined as opposite over adjacent, which corresponds to height over base distance.
Show transcript
[Slide 1] Understanding Two-Position Problems
Welcome students. In these problems, the object height is constant, but you move closer or further. We use two angles of elevation to find the unknown height.
[Slide 2] Step-by-Step Method
First, sketch the scenario showing two observation points. Identify the common height shared by both triangles. Then write the tangent equation for each position separately.
[Slide 3] Solved Example with Numbers
Let's solve a tower problem. Angles are thirty and sixty degrees, with twenty meters gap. Substituting values gives us the height as twenty root three meters.
[Slide 4] Watch Out for Errors
Students often forget that the base lengths differ by the walking distance. Ensure you subtract the smaller distance from the larger one correctly. Also, check which trig ratio applies.
[Slide 5] Key Takeaways
Remember the height is the same link between triangles. Use the difference in base lengths to solve. Practice these steps for board exams.