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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