A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first row of seats is placed 9 ft from the screen and the rows are set 3 ft apart. The floor of the seating area is inclined at an angle of a = 20° above the horizontal and the distance up the incline that you sit is x. The theater has 21 rows of seats, so 0 < x< 60. Suppose you decide that the best place to sit is in the row where the angle 0 subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 ft above the floor, as shown in the figure. 1. Show that a? + b2 - 625 arccos 2ab where a? = (9 + x cos a)² + (31 – x sin a)² and b? = (9 + x cos a)² + (x sin a – 6) 2. Use a graph of 0 as a function of x to estimate the value of x that maximizes 0. In which row should you sit? What is the viewing angle 0 in this row?

A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first row of seats is placed 9 ft from the screen and the rows are set 3 ft apart. The floor of the seating area is inclined at an angle of a = 20° above the horizontal and the distance up the incline that you sit is x. The theater has 21 rows of seats, so 0 < x< 60. Suppose you decide that the best place to sit is in the row where the angle 0 subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 ft above the floor, as shown in the figure. 1. Show that a? + b2 - 625 arccos 2ab where a? = (9 + x cos a)² + (31 – x sin a)² and b? = (9 + x cos a)² + (x sin a – 6) 2. Use a graph of 0 as a function of x to estimate the value of x that maximizes 0. In which row should you sit? What is the viewing angle 0 in this row?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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.

Question

A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first
row of seats is placed 9 ft from the screen and the rows are set 3 ft apart. The floor of the
seating area is inclined at an angle of a = 20° above the horizontal and the distance up the
incline that you sit is x. The theater has 21 rows of seats, so 0 < x< 60. Suppose you decide
that the best place to sit is in the row where the angle 0 subtended by the screen at your eyes
is a maximum. Let's also suppose that your eyes are 4 ft above the floor, as shown in the
figure.
1. Show that
a² + b2 – 625
arccos
2ab
where
a? = (9 + x cos a)² + (31 – x sin a)²
and
b? = (9 + x cos a)² + (x sin a – 6)²
2. Use a graph of 0 as a function of x to estimate the value of x that maximizes 0. In which
row should you sit? What is the viewing angle 0 in this row?

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