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How far should you stand from artwork to have the maximum viewing angle?

Questions 1-8 of pg 231-232 continued

Questions 1-8 of pg 231-232

Questions 1-8 of pg 231-232 continued

Evaluate- Question 7

No I didn't find any systems or rules or shortcuts I could find on my calculator that could have helped me, now I'm starting to wonder whether I'm right or wrong. Hopefully I've done the right method to find the different values of V. That could have made a huge difference as this took me a few hours to complete

Evaluate- Question 6

a) How confident are you that you have found the largest value for V? Well I'm so confident that I have the evidence to back it up from the workings out from the sheet I sketched my table and drawing out of. At first I thought it was one but then I found the key that it didn't exactly have to be a whole number.

b)What could you do to improve your answer? Well I could even try getting really specific and trying two decimal placed numbers to try and get a bigger number than the ones I came up with. For example instead of 1.1m maybe using a much more specific 1.15m or a 1.25m

Engage- Question 1

Use the two triangles and the measurements in the diagram to calculate A, B and then V if the person viewing the artwork is standing a distance d of 3m from the wall.

Working out:

Tan = O/A Tan = O/A V = A-B

Tan B = 1/3 Tan A = 2/3 = 33.69 deg.-18.43 deg.

B = Tan -1 (1/3) A = Tan -1 (2/3) = 15.26 deg.

= 18.43 = 33.69

15.26 degrees was the amount V was, angle B equaled 18.43 degrees and angle A equaled 33.69 degrees.

It is very essential that you are standing the ideal distance away to get the full picture and detail of what you are viewing. If you stand too close then you're cramped, you're neck gets sore and you don't get the full detail. If you stand too far away then you then cannot view the detail extremely well and then you don't receive the feelings and messages the artist is trying to get the viewer to feel and understand. The whole reason of this investigation is to find the ideal distance to stand as to find the ideal distance will then enable us to gather the most information we possibly can and therefore gives us, the viewer, a greater advantage.

Questions 1-8 of pg 231-232 continued

Conclusion

Questions 1-8 of pg 231-232 continued

Explain- Question 3

Describe any pattern or trend you can see in the values of angles A, B and V as you move closer to or further away from the wall.

I did find out that the A, B and V angle values all respectively decreased when we got further away from the artwork. This really makes sense as when you are standing closer to the artwork you have to tilt your head more degrees than when you are further away from the artwork to get the full picture. For example, value of V for 6 metres= 8.97 degrees whereas value for V for 15 metres= 3.78 degrees.

Extend- Question 8

Investigate how a person's height affects where they should stand to gain the maximum viewing angle (i.e. where a short person should stand compared to a tall person).

These tables used the same working out as the working outs above it but with different values respectively. As you can observe the taller person will have a much better viewing angle as his/her eye-level will be slightly higher than the short person.

So I draw to the conclusion definitely knowing that the largest value for V doesn't in fact come from the number 1 and that it comes from a one decimal placed number not a whole number as all whole numbers tested had started to decrease in maximum viewing angle which then i crossed off my list of numbers to give thought to. So the big question then comes down to this, that to view the artwork you must stand at least either a distance away that is the eye-level length plus the length of the artwork. Or if it has unit figured decimal placed numbers then you must stand as close as the 1m mark otherwise stand in between the length of the artwork.

Questions 1-8 of pg 231-232 continued

Explore- Question 2

By changing the value of d find the largest possible value for V. Try at least five values for d

The table below indicates the 6 values I tried to find the largest value for V. The largest I found was from a distance of 1 metre which equaled 18.43. I used the same formula as question 1

Questions 1-8 of pg 231-232 continued

Elaborate- Question 4

Use different values of d to find the best viewing position for:

a) a 0.75m tall painting mounted 1.2m above eye-level. A: The highest value for V came from a distance of 1.95m away from the painting, which I believe is the best spot as it is the only point where it rose.

b) a 1.5m tall painting mounted 0.8m above eye-level.A: The highest value for V came from a distance of 1.15m away from the painting, which I believe is the best spot as it is the only point where it rose.

c) a 63cm (0.63m) tall painting mounted 50cm(0.5m) above eye-level.A: The highest value for V came from a distance of 1.13m away from the painting, which I believe is the best spot as it is the only point where it rose.

Elaborate- Question 5

Summarise your findings and answer the big question.

Well I believe you should stand the length of the art work and above eye-level length away to view it well for example if a painting is 1.2m but it is raised 0.5m above the eye-level then that means you should stand the a distance of the sum of those two numbers away(1.7). I found that when I did use the method above, it came up with a V value bigger than standing 1m away which then made me think why this is the case which I then tested for 2m and it decreased. Fingers crossed I'm right about this. For part b) I tried to get as close to 1 and got an answer with the most viewing angle

Year 10 Trigonometry Investigation Viewing Artwork-Where should you stand?

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