A Painting in an Art Gallery Has Height $h$ And Is Hung So That Lower Edge Is a Distance

question 55

Multiple Choice

A painting in an art gallery has height $h$ and is hung so that lower edge is a distance $d$ above the eye of an observer (as in the figure) . How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle $\theta$ subtended at his eye by the painting?)

• A) \(x = \sqrt { h ( d + h ) }\)
• B) \(x = h ^ { 2 } ( h + d ) ^ { 2 }\)
• C) \(x = d ^ { 2 } ( h + d ) ^ { 2 }\)
• D) \(x = \sqrt { d ( h + d ) }\)
• E) \(x = h ^ { 2 } ( h - d ) ^ { 2 }\)

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Definitions:

Endorphin

Natural peptides produced by the brain that act as neurotransmitters to reduce pain perception and lead to feelings of euphoria.

Serotonin

A neurotransmitter that contributes to feelings of well-being and happiness, also involved in the regulation of mood, sleep, and appetite.

Substance P

A neuropeptide involved in the transmission of pain and other sensory signals to the brain, also implicated in inflammatory processes.

Endorphins

Neurotransmitters produced by the nervous system to cope with pain or stress, often described as "natural painkillers."