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

question 29

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:

Lower Court

A court with limited jurisdiction, whose decisions may be reviewed by higher courts, also known as inferior or trial courts.

Common Law

A legal system based on precedent and judicial decisions rather than statutory laws, forming the basis of the legal system in the UK, the US, and other countries.

Case Law

The body of past judicial decisions from courts that guide future rulings on similar legal questions or disputes.

Statutory Law

Law enacted by a legislative body, such as Congress or a state legislature, as opposed to common law or constitutional law.