Answer:
The distance between the walls is 70 m.
Step-by-step explanation:
Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is
BE ⊥ ED and CD ⊥ ED
AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m
AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.
The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°
The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°
As shown is figure attached below.
WE have to find the distance between the walls that is Length of ED
Length of ED = EA + AD
Consider the Δ AEB,
Using trigonometric ratio,
[tex]\tan\theta=\frac{perpendicular}{base}[/tex]
Here [tex]\theta=45^{\circ}[/tex] , perpendicular = 30 m and base we can find.
thus,
[tex]\tan 45^{\circ}=\frac{30}{EA}[/tex]
We know [tex]\tan 45^{\circ}=1[/tex]
thus, EA = 30 m
Consider the Δ AEB,
Using trigonometric ratio,
[tex]\cos\theta=\frac{base}{hypotenuse}[/tex]
Here [tex]\theta=60^{\circ}[/tex] , hypotenuse = 80 m and base we can find.
thus, [tex]\cos 60^{\circ}=\frac{base}{80}[/tex]
We know, [tex]\cos 60^{\circ}=\frac{1}{2}[/tex]
thus, Base = 40 m
AD = 40 m
Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m
