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

question 87

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:

Break-even Price

The price level at which total revenues are equal to total costs, resulting in neither profit nor loss.

Economic Losses

The decrease in economic value arising from factors such as poor decisions, market shifts, or external disruptions affecting profitability.

Fixed Costs

Costs that do not vary with the level of output or sales, such as rent, salaries, and insurance.

Average Total Cost

The sum of all production costs divided by the quantity of output produced, encompassing both fixed and variable costs, giving a comprehensive cost per unit.