Boris is sitting in a movie theatre, 11 meters from the screen. The angle of elevation from his line of sight to the top of the screen is 13degrees, and the angle of depression from his line of sight to the bottom of the screen is 49degrees?

Question

Find the height of the entire screen? Round to the nearest tenth.

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Answer 1 · 2018-06-13T00:50:57

#"Screen height " = 15.2 " meters"#

Anjali G

Using the variable definitions of #a# and #b# as shown in the diagram above, we can use trigonometry to solve for the height of the screen, #a+b#.

#tan(13^@) = a/11#

#a = 11tan(13^@)#

#tan(49^@) = b/11#

#b = 11tan(49^@)#

Therefore, the height of the screen #a+b# is:

#a + b = 11tan(13^@)+11tan(49^@)#

#a+b = 2.5396 + 12.6541#

#a+b = 15.1936 " meters"#