Question

The lower edge of a painting, 10 ft in height, is 2 ft above an observer’s eye level. assuming that the best view is obtained when the angle subtended at the observer’s eye by the painting is maximum, how far from the wall should the observer stand?

a) 5 ft
b) 10 ft
c) 15 ft
d) 20 ft

Answer 1

For the best view of the painting, where the angle subtended at the observer's eye by the painting is maximum, the observer should stand 5 ft from the wall.

Step-by-step explanation:

The question asks where an observer should stand for the best view of a painting, which describes a problem that can be solved using principles of optimal viewing angle and basic trigonometry.

The distance at which the observer should stand from the wall is the distance where the angle subtended by the painting at the observer's eye is maximized. This occurs when the observer's line of sight to the top and bottom edges of the painting makes equal angles with the normal (a line perpendicular to the wall), forming an isosceles triangle. Since the painting is 10 ft high and its lower edge is 2 ft above eye level, the observer's eye level is effectively at the midpoint of the painting. In such situations, the optimal distance from the wall to the observer is equal to half the height of the painting.

Therefore, the observer should stand 5 ft from the wall for the best view.