Question 1193190
Certainly, let's analyze, solve, and answer the problem about the tilted scarecrow.

**1. Draw a Diagram:**

[Image of a diagram showing a tilted scarecrow casting a shadow. 
* The scarecrow is tilted at an angle of 12° from the vertical.
* The shadow of the scarecrow is 3 meters long.
* The angle of elevation from the tip of the shadow to the top of the scarecrow is 27°. 
* Label the height of the scarecrow as 'h', the length of the shadow as 's', and the angle of tilt as 'θ'.]

**2. Determine the Length of the Scarecrow:**

* **Analyze:**
    * We have a right triangle formed by the scarecrow, its shadow, and the ground.
    * We know the angle of elevation (27°) and the length of the shadow (3 meters).
    * We need to find the height of the scarecrow (h).

* **Solve:**
    * Using the tangent function in trigonometry:
        * tan(27°) = h / 3 
        * h = 3 * tan(27°) 
        * h ≈ 1.52 meters

* **Answer:** The length of the scarecrow is approximately 1.52 meters.

**3. Determine the Angle of Tilt for Different Shadow Lengths:**

* **Analyze:**
    * The angle of elevation remains constant at 27°.
    * We need to find the angle of tilt (θ) for different shadow lengths.

* **Solve:**
    * **For a shadow length of 2 meters:**
        * tan(27°) = h / 2
        * h = 2 * tan(27°) 
        * h ≈ 1.01 meters 
        * Now, we have a right triangle with the height (h) and the angle of elevation (27°). 
        * We can use the tangent function to find the angle of tilt (θ): 
            * tan(θ) = h / 3 
            * tan(θ) = 1.01 / 3 
            * θ = arctan(1.01 / 3) 
            * θ ≈ 18.58°

    * **For a shadow length of 1 meter:**
        * tan(27°) = h / 1
        * h = 1 * tan(27°) 
        * h ≈ 0.51 meters 
        * tan(θ) = h / 3 
        * tan(θ) = 0.51 / 3 
        * θ = arctan(0.51 / 3) 
        * θ ≈ 9.61°

* **Answer:**
    * If the shadow length is 2 meters, the angle of tilt is approximately 18.58°.
    * If the shadow length is 1 meter, the angle of tilt is approximately 9.61°.

**Note:** These calculations assume that the scarecrow remains rigid and only tilts at its base. 

I hope this helps! Let me know if you have any other questions.