54. Viewing Angle of an Observer While visiting a museum, an observer views a painting that is 3 ft high and hangs 6 ft above the ground. See the figure. Assume her eyes are 5 ft above the ground, and let x be the distance from the spot where she is standing to the wall displaying the painting. 3 ft 6 ft 5 ft x ft (a) Show that 0, the viewing angle subtended by the painting, is given by 0 = tan¬1 tan (6)- (b) Find the value of x to the nearest hundredth for each value of 0. (i) 0 = 6 (ii) 0 = 8 (c) Find the value of 0 to the nearest hundredth for each value of x. (i) x = 4 (ii) x = 3
54. Viewing Angle of an Observer While visiting a museum, an observer views a painting that is 3 ft high and hangs 6 ft above the ground. See the figure. Assume her eyes are 5 ft above the ground, and let x be the distance from the spot where she is standing to the wall displaying the painting. 3 ft 6 ft 5 ft x ft (a) Show that 0, the viewing angle subtended by the painting, is given by 0 = tan¬1 tan (6)- (b) Find the value of x to the nearest hundredth for each value of 0. (i) 0 = 6 (ii) 0 = 8 (c) Find the value of 0 to the nearest hundredth for each value of x. (i) x = 4 (ii) x = 3
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Transcribed Image Text:54. Viewing Angle of an Observer While visiting a museum, an observer views a
painting that is 3 ft high and hangs 6 ft above the ground. See the figure. Assume
her eyes are 5 ft above the ground, and let x be the distance from the spot where she
is standing to the wall displaying the painting.
3 ft
6 ft
5 ft
x ft
(a) Show that 0, the viewing angle subtended by the painting, is given by
(:)
0 = tan¬1
tan
(6)-
(b) Find the value of x to the nearest hundredth for each value of 0.
(i) 0 =
6
(ii) 0 =
8
(c) Find the value of 0 to the nearest hundredth for each value of x.
(i) x = 4
(ii) x = 3
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