Chapter 1: Problem 52

Angular measure describes how far apart two objects appear to an observer. From where you are currently sitting, estimate the angular distance between the floor and the ceiling at the front of the room you are sitting in, the angular distance between the two people sitting closest to you, and the angular size of a clock or an exit sign on the wall. Draw sketches to illustrate each answer and describe how each of your answers would change if you were standing in the very center of the room.

Short Answer

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From a seated position, the angular distances between the floor and ceiling, between two people, and the angular size of a clock or exit sign would be estimated using hands or fingers for measuring. If standing in the center of the room, the angular distance between the floor and ceiling remains the same while the distances between two people and the clock or exit sign become smaller as the observer is further away.

Step by step solution

Definition of Angular Distance and Size

Angular distance is the amount of separation between two points as perceived from an observer’s point of view, defined by the angle starting from one point and ending at another. Similarly, the angular size is the apparent size of an object as perceived from an observer’s point of view, typically expressed as an angle.

Estimating Angular Distance and Size

Without any specific measurements to work with, estimation becomes a guessing process based on what is already known and then predicting the answer. Using hands or fingers can be an effective way of estimating the angles. For example, for estimating the angular size or distance between the floor and the ceiling, an extended hand with fingers spread might help.

Drawing Sketches

Draw rough sketches to illustrate these estimations. Create three sketches: one for floor to ceiling, one for the two people, and one for the clock or exit sign.

Predict Changes

Considering how the answers would change if standing at the center of the room, the angular distance between the floor and the ceiling would be the same since height of the room remains the same. As for the two people and clock or exit sign, those angular distances likely become smaller because standing further away from objects generally makes them appear closer together or smaller.

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Short Answer

Step by step solution

Definition of Angular Distance and Size

Estimating Angular Distance and Size

Drawing Sketches

Predict Changes

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