Answer:
103.92 m
Step-by-step explanation:
Refer the attached figure.
A source of laser light sends rays AB and AC toward two opposite walls of a hall.
A source of laser light is at point A on the ground between two parallel walls.
The walls are perpendicular to the ground.
AB is a ray of light which strikes the wall on the left at point B which is 60 meters above the ground i.e. BD = 60 m
AC is a ray of light which strikes the wall on the right at point C which is 40 m above the ground i.e. CE = 40 m
The ray AB makes an angle of 60 degrees with the ground i.e. ∠BAD = 60°
The ray AC makes an angle of 30 degrees with the ground.i.e. ∠CAE=30°
We are required to find the distance between the two walls i.e. DA=DA+AE
In ΔABD
Perpendicular = BD = 60 m
Base = AD
∠BAD = 60°
To find AD we will use trigonometric ratio
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan60^{\circ}= \frac{BD}{AD}[/tex]
[tex]\sqrt{3}= \frac{60}{AD}[/tex]
[tex]AD= \frac{60}{\sqrt{3}}[/tex]
In ΔCAE
Perpendicular = CE = 40 m
Base = AE
∠CAE=30°
To find AE we will use trigonometric ratio
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
[tex]tan30^{\circ}= \frac{CE}{AE}[/tex]
[tex]\frac{1}{sqrt{3}}= \frac{40}{AE}[/tex]
[tex]AE= 40\sqrt{3}[/tex]
Thus the distance between walls = DA=DA+AE
=[tex] \frac{60}{\sqrt{3}}+40\sqrt{3}[/tex]
=[tex] 103.923[/tex]
Thus the distance between the two walls is 103.92 m
Hence Option C is correct.
