Goran is sitting in a movie theater, 5 meters from the screen. The angle of elevation from his line of sight to the top of the s creen is 18, and the angle of depression from his line of sight to the bottom of the screen is 48. Find the height of the entire screen.
1 answer:
Answer:
Approximately
Height of screen= 7.1 meters
Step-by-step explanation:
Angle of elevation= 18°
Angle of depression= 58°
Distance of Goran from screen= 5 m
Height of screen from the attachment below
X+y
First let's determine angle a and b
a= 180-90-18
a= 72°
b= 180-90-48
b= 43°
Using sine formula
5/sin a= x/sin 18
5/sin 72= x/sin18
(5*sin 18)/sin 72= x
1.6246 = x
X= 1.6246 m
Y/sin 48= 5/sin b
Y= (5*sin 48)/sin 43
Y= (5*1.08965779)
Y= 5.4483 m
Height of screen= x+y
Height of screen= 1.6246+5.4483
Height of screen= 7.0729
Approximately
Height of screen= 7.1 meters
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