(b) A poster hanging on a wall has a vertical height 3.66 m. From a point 5 m away from the wall on the same plane, the angle of elevation of the bottom edge of the poster was found to be 45°. What will be the angle of elevation of the top edge of the poster if it is observed from the same point on the horizontal plane?  Ans60

We can solve this problem by applying basic trigonometry principles to determine the angle of elevation to the top edge of the poster.

### Step-by-step solution:

1. **Given dataWe can solve this problem by applying basic trigonometry principles to determine the angle of elevation to the top edge of the poster.

### Step-by-step solution:

1. **Given **
   - The height of the poster: \( h_{\text{poster}} = 3.66 \, \text{m} \)
   - Distance from the observer to the wall: \( d = 5 \, \text{m} \)
   - Angle of elevation to the bottom of the poster: \( \theta_{\text{bottom}} = 45^\circ \)

2. **Determine the height of the bottom of the poster:**
   Since the angle of elevation to the bottom is 45° and the distance to the wall is 5 m, we can use the tangent function.

   \[
   \tan(45^\circ) = \frac{h_{\text{bottom}}}{d}
   \]

   Since \( \tan(45^\circ) = 1 \), we have:

   \[
   1 = \frac{h_{\text{bottom}}}{5}
   \]

   Therefore, the height of the bottom of the poster from the ground is:

   \[
   h_{\text{bottom}} = 5 \, \text{m}
   \]

3. **Determine the height of the top of the poster:**
   The total height of the top of the poster above the ground will be the height of the bottom of the poster plus the height of the poster itself:

   \[
   h_{\text{top}} = h_{\text{bottom}} + h_{\text{poster}} = 5 + 3.66 = 8.66 \, \text{m}
   \]

4. **Find the angle of elevation to the top of the poster:**
   Using the tangent function again to find the angle of elevation to the top edge of the poster:

   \[
   \tan(\theta_{\text{top}}) = \frac{h_{\text{top}}}{d}
   \]

   Substituting the known values:

   \[
   \tan(\theta_{\text{top}}) = \frac{8.66}{5}
   \]

   \[
   \tan(\theta_{\text{top}}) = 1.732
   \]

5. **Calculate the angle:**

   \[
   \theta_{\text{top}} = \tan^{-1}(1.732)
   \]

   Using a calculator:

   \[
   \theta_{\text{top}} \approx 60^\circ
   \]

Thus, the angle of elevation to the top edge of the poster is approximately **60°**.

---

Do you have any questions or need further details on the explanation?

### Relative Questions:
1. What is the significance of the tangent function in angle of elevation problems?
2. How would the solution change if the distance from the wall was doubled?
3. Can you explain why \( \tan(45^\circ) = 1 \) for any right triangle?
4. How could this problem be adapted if the poster was at an angle rather than vertical?
5. What if the observer was not on the same plane but higher up, how would we approach it?

### Tip:
Always double-check which sides of the right triangle correspond to the angles and distances to avoid confusion with the tangent function!

A poster hanging on a wall has a vertical height 3.66 m. From a point 5 m away from the wall on the same plane, the angle of elevation of the bottom edge of the poster was found to be 45°. What will be the angle of elevation of the top edge of the poster if it is observed from the same point on the horizontal plane? Ans60

Solve a problem involving the calculation of the angle of elevation to the top of a 3.66 m tall poster from a point 5 m away using trigonometry. The solution applies the tangent function and angle of elevation concepts, suitable for students in Grades 9-12.

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