Q9. A park has 2 flagpoles 20m apart. One pole is 12m high and the other is 27m high.
Calculate the angle of depression from the top of the taller pole to the top of the shorter
pole.

To calculate the angle of depression from the top of the taller pole to the top of the shorter pole, we can approach the problem using trigonometry.

### Step-by-Step Solution:

1. **Visualize the scenario**:
   - There are two flagpoles.
     - Pole 1 is 12 meters high.
     - Pole 2 is 27 meters high.
   - The distance between the two poles at ground level is 20 meters.
   - We are asked to calculate the **angle of depression** from the top of the taller pole (27 m) to the top of the shorter pole (12 m).

2. **Identify the height difference**:
   The height difference between the two poles is:
   \[
   \Delta h = 27 - 12 = 15 \text{ meters}
   \]

3. **Right triangle setup**:
   We can model this as a right triangle:
   - The vertical leg of the triangle is the height difference, \(\Delta h = 15\) meters.
   - The horizontal leg of the triangle is the distance between the two poles, which is 20 meters.
   - The angle of depression, \(\theta\), is what we need to find.

4. **Use the tangent function**:
   The tangent of the angle of depression is the ratio of the opposite side (height difference) to the adjacent side (distance between poles):
   \[
   \tan(\theta) = \frac{\Delta h}{20} = \frac{15}{20} = 0.75
   \]

5. **Find the angle**:
   To find \(\theta\), take the arctangent (inverse tangent)

A park has 2 flagpoles 20m apart. One pole is 12m high and the other is 27m high. Calculate the angle of depression from the top of the taller pole to the top of the shorter pole.

Learn how to calculate the angle of depression from the top of a 27m flagpole to a 12m flagpole 20m away using trigonometry. This step-by-step solution explains how to use the tangent function and arctangent to solve this real-world problem. Ideal for students in Grades 9-12.

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