Question

A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B and C, as shown below: 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. AC is a ray of light which strikes the wall on the right at point C which is 40 m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 30 degrees with the ground. What is the distance between the walls? 110.90 m 149.28 m 103.92 m 173.20 m

Answer 1

The answer is 103.92m

Answer 2

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

$tan\theta = \frac{Perpendicular}{Base}$

$tan60^{\circ}= \frac{BD}{AD}$

$\sqrt{3}= \frac{60}{AD}$

$AD= \frac{60}{\sqrt{3}}$

In ΔCAE

Perpendicular = CE = 40 m

Base = AE

∠CAE=30°

To find AE we will use trigonometric ratio

$tan\theta = \frac{Perpendicular}{Base}$

$tan30^{\circ}= \frac{CE}{AE}$

$\frac{1}{sqrt{3}}= \frac{40}{AE}$

$AE= 40\sqrt{3}$

Thus the distance between walls = DA=DA+AE

                                                         =$\frac{60}{\sqrt{3}}+40\sqrt{3}$

                                                         =$103.923$

Thus the distance between the two walls is 103.92 m

Hence Option C is correct.