Optimal Painting Height for Maximum Viewing Comfort | 3m Viewing Distance

[acidxc]

hi,
can someone help me on 1 question i have been really trying and don't seem to know how to do it here is the question;

Francis is hanging a painting on a wall, he wants the height on the center of the painting to be located so that no visiors need to look up or down more the 5 degrees to viwer the center of the painting when standing 3 m away. If he expects visitors eyes to be between 152 cm to 200 cm off the ground. What is the range of heights that he can hang the center of the painting, to the nearest centimeter

So far i have done the following iam not sure if its the right start

x

 

[HallsofIvy]

Your picture is wrong. I presume that the vertical line labeled "200 cm" on the left represents the picture. You are told "no visiors need to look up or down more the 5 degrees to viwer the center of the painting when standing 3 m away" and that "he expects visitors eyes to be between 152 cm to 200 cm off the ground". You should have two lines drawn from the center of the picture to a vertical line 3 m away-one up to a height 200 cm, the other down to a height 152 cm. In other words, you should have a triangle with vertex at the center of the picture, vertical side of length 200- 152= 48 cm and base angles of 5 degrees. If you draw a horizontal line from the lower end of that vertical 48 cm line, representing the eyes of the shortest person, you have a right triangle with angle 5 degrees and near side 3 m= 300 cm. The opposite side is the height above that persons eyes (152 cm) to the center of the picture. Adding 152 to that will give the height of the center of the picture above the floor.

 

[Architeuthis Dux]

= height of painting

Hello Francis,

Thank you for your question. I understand the importance of considering viewing comfort when hanging a painting. To determine the optimal height for maximum viewing comfort, we need to take into account the distance between the viewer and the painting, as well as the average height of the viewer's eyes.

Based on the information provided, the optimal painting height should be located so that viewers do not need to look up or down more than 5 degrees when standing 3 meters away. This means that the center of the painting should be at eye level for viewers standing at a distance of 3 meters.

To find the range of heights that the center of the painting can be hung at, we can use the following equation:

x = tan(5) * 3

Where x is the height of the painting and 5 represents the maximum angle of deviation from eye level.

Using this equation, we can calculate that the center of the painting can be hung at a height of approximately 26.18 cm (to the nearest centimeter) from the ground. However, we also need to consider the range of heights of the viewer's eyes, which is between 152 cm to 200 cm off the ground.

Therefore, the range of heights that the center of the painting can be hung at is between 152 cm + 26.18 cm = 178.18 cm and 200 cm + 26.18 cm = 226.18 cm off the ground. This means that the painting can be hung anywhere between 178 cm to 226 cm off the ground, to the nearest centimeter, to ensure maximum viewing comfort for all visitors.

I hope this helps you in determining the optimal height for your painting. Let me know if you have any further questions.

Best,