High School

We appreciate your visit to A photographer wants to take a picture of a 4 foot vase standing on a 3 foot pedestal She wants to position the camera at. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A photographer wants to take a picture of a 4-foot vase standing on a 3-foot pedestal. She wants to position the camera at point C on the floor so that the angles subtended by the vase and the pedestal are the same size. How far away from the foot of the pedestal should the camera be?

A. 8.1 ft
B. 6.3 ft
C. 7.9 ft
D. 4.8 ft

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]

Thanks for taking the time to read A photographer wants to take a picture of a 4 foot vase standing on a 3 foot pedestal She wants to position the camera at. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada