Solve the Problem $\theta$ To an Observer, Where $\theta = \tan ^ { - 1 } \left( \frac { \mathrm { x } } { \mathrm { x } ^ { 2 } + 1.8 } \right)$

question 69

Multiple Choice

Solve the problem.
-A painting 1 meter high and 3 meters from the floor will cut off an angle $\theta$ to an observer, where $\theta = \tan ^ { - 1 } \left( \frac { \mathrm { x } } { \mathrm { x } ^ { 2 } + 1.8 } \right)$ , assuming that the observer is $x$ feet from the wall where the painting is displayed and that the eyes of the observer are $1.8$ meters above the ground (see the figure) . Find the value of $\theta$ for $x = 2$ . Round to the nearest tenth of a degree.

• A) \(27.8 ^ { \circ }\)
• B) \(19.0 ^ { \circ }\)
• C) \(21.5 ^ { \circ }\)
• D) \(16.5 ^ { \circ }\)

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Definitions:

Von Restorff Effect

A psychological phenomenon where an item that noticeably stands out is more likely to be remembered than other items.

Essay Exam

A type of test where individuals are required to write comprehensive and detailed responses to questions or prompts.

Free Recall

A test of memory in which an individual is asked to remember information without explicit prompts or cues.

Nonsense Syllables

A set of letters that do not form a known word, used in psychological experiments to study memory and learning processes by eliminating association effects.