the create the illusion of a life-sized image, puppeteers sometimes use a light source to show an enlarged image of. puppet projected on a screen or wall. Suppose the the distance between a light source l and the upper is 24 inches, LP. TO what distance PP' should you place the puppet from the green to create a 49.5 inch tall shadow I'M' from a 9 inch puppet
(a triangle is created by the light source, L connected to I and M as the legs. These are also points are extended to create another line segments, LI' and LM') please help!
assuming "upper" means "puppet" and "green" means "screen" and M is the top of the puppet, then I guess we have
9/24 = 49.5/(24 + PP')
Now just solve for PP'
Your description of the scene is murky, to say the least ...
To solve this question, we need to use similar triangles and proportions. Let's break down the given information and steps to find the solution:
1. We have a triangle formed by the light source (L), the puppet's head (P), and the point where the puppet meets the ground (I). This triangle is similar to another triangle formed by the light source (L), the puppet's shadow head (P'), and the point where the shadow meets the ground (I').
2. We are given the distance between the light source (L) and the upper part of the puppet (P) as 24 inches (LP).
3. We are asked to find the distance between the puppet's head (P) and the point where the puppet's shadow head (P') should be placed in order to create a 49.5-inch tall shadow (I'M') from a 9-inch puppet.
To find the solution:
1. Write down the proportion considering the similar triangles:
(LP) / (LI) = (LP') / (LI')
2. Substitute the known values into the proportion:
24 / 9 = (PP' + 49.5) / 49.5
3. Solve for PP':
Cross-multiply and solve the equation:
(24 * 49.5) / 9 = PP' + 49.5
PP' = (24 * 49.5) / 9 - 49.5
4. Simplify the equation:
PP' = 49.5 * (24 / 9 - 1)
5. Calculate the value:
PP' = 49.5 * (2.6667 - 1)
PP' = 49.5 * 1.6667
PP' ≈ 82.5 inches
Therefore, you should place the puppet at a distance of approximately 82.5 inches from the green wall or screen to create a 49.5-inch tall shadow from a 9-inch puppet when the light source is 24 inches away from the puppet's head.