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14 A picture TB that is 1 metre tall is hung on a wall so that its bottom edge B is 3 metres above the eye E of a viewer. Let the distance EP be x metres, and 1 m В let 0 be the angle that the picture subtends at E. a Show that 0 = tan- – tan-. 3 m b Show that 0 is maximised when the viewer is 2v3 metres from the wall. c Show that the maximum angle subtended by the picture at E is tan-1 . Ε x P

14 A picture TB that is 1 metre tall is hung on a wall so that its bottom edge B is 3 metres above the eye E of a viewer. Let the distance EP be x metres, and 1 m В let 0 be the angle that the picture subtends at E. a Show that 0 = tan- – tan-. 3 m b Show that 0 is maximised when the viewer is 2v3 metres from the wall. c Show that the maximum angle subtended by the picture at E is tan-1 . Ε x P

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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T 14 A picture TB that is 1 metre tall is hung on a wall so that its bottom edge B 1 m is 3 metres above the eye E of a viewer. Let the distance EP be x metres, and В let 0 be the angle that the picture subtends at E. a Show that 0 = tan 3 m b Show that 0 is maximised when the viewer is 2v3 metres from the wall. c Show that the maximum angle subtended by the picture at E is tan¬'R: -1 V3 E P
Transcribed Image Text:T 14 A picture TB that is 1 metre tall is hung on a wall so that its bottom edge B 1 m is 3 metres above the eye E of a viewer. Let the distance EP be x metres, and В let 0 be the angle that the picture subtends at E. a Show that 0 = tan 3 m b Show that 0 is maximised when the viewer is 2v3 metres from the wall. c Show that the maximum angle subtended by the picture at E is tan¬'R: -1 V3 E P
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