Explanation Given: A person 6 ft tall is watching a street light 18 ft high while walking toward it at a speed of 5 ft/s, s shown in figure 3.47. Calculation: Draw the figure and assign the variables to the quantities that vary. Let x is the distance and θ is an angle of elevation at time ‘t’ Find d θ d t when x = 9 ft From the formula that relates the variables. From the right triangle, tan θ = 12 x If x = 9 , then tan θ = 12 9 → csc θ = 15 12 Differentiate the equation tan θ = 12 x x = 12 cot θ d x d t = − 12 csc 2 θ d θ d t Substitute specific numerical values and solve algebraically for any required rate

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Chapter 3.7, Problem 53PS

To determine

To find: the rate of change in the angle of elevation of the person’s line of with respect to time when the person is 9 ft from the base of the light.

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Chapter 3.7, Problem 52PS

Chapter 3.7, Problem 54PS

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Chapter 3 Solutions

Calculus

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the rate of change in the angle of elevation of the person’s line of with respect to time when the person is 9 ft from the base of the light.

Solution Summary: The author calculates the rate of change in the angle of elevation of a person's line of with respect to time when they are 9 ft from the base of the light.

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To find: the rate of change in the angle of elevation of the person’s line of with respect to time when the person is 9 ft from the base of the light.

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Chapter 3 Solutions