Answer :
The camera should be positioned 12 feet away from the foot of the pedestal. Therefore, the correct answer is not among the given options.
To solve this problem, we need to position the camera at a point where the angles subtended by both the vase and the pedestal are the same. We will use the concept of similar triangles for this purpose.
- Given:
Height of the vase ([tex]h_1[/tex]) = 4 feet
Height of the pedestal ([tex]h_2[/tex]) = 3 feet
Total height ([tex]h_1 + h_2[/tex]) = 7 feet
Let's denote the distance from the foot of the pedestal to the point where the camera should be placed as [tex]d[/tex]. Since the angles subtended by the vase and the pedestal must be equal, we can use the tangent function for the angles.
- The tangent of the angle subtended by the vase is given by:
[tex]\tan(\theta) = \frac{4}{d}[/tex]
- The tangent of the angle subtended by the pedestal is given by:
[tex]\tan(\theta) = \frac{3}{d}[/tex]
- Since these two angles are equal, their tangents must be equal:
[tex]\frac{4}{d} = \frac{3}{d - x}[/tex]
Where [tex]x[/tex] is the height of the pedestal, [tex]x = 3[/tex] feet.
- Let's solve for [tex]d[/tex]:
[tex]4(d - 3) = 3d[/tex]
[tex]4d - 12 = 3d[/tex]
[tex]d = 12[/tex]
