# Asource 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. the length of ab is 60m. ac is a ray of light which strikes the wall on the right at point c which is 40m above the ground. the ray ab makes an angle of 60 degrees with the ground. the ray ac makes an angle of 45 degrees with the ground. what is the distance between the walls? 80 m 140 m 70 m 110 m

70 m

Step-by-step explanation:

AB makes a 30-60-90 triangle with the wall.

AC makes a 45-45-90 triangle with the wall.

In a 30-60-90 triangle, the short leg (opposite of the 30° angle) is half the hypotenuse.

In a 45-45-90 triangle, the legs are the same length.

So the distance between the left wall and the laser is 60/2 = 30 m.

The distance between the right wall and the laser is 40 m.

The total distance is therefore 70 m.

70 meters.

Step-by-step explanation:

Observe the figure attached.

The distance between the walls is:

Both triangles are right triangles. Therefore, you can calculate the distance between the walls as following:

- Calculate the distance AD:

- Calculate the distance AE:

Therefore the distance between the walls is:

70m

Step-by-step explanation:

For wall from the left, we have a right triangle and hypotenuse is 60 and the adjacent leg is what we want to find. The angle is 60°

cos60 = x/60

1/2 = x /60

2x = 60

x = 30

For wall from the right, we have a right triangle and opposite leg is 40 and the adjacent leg is what we want to find. The angle is 45°

tan45 = 40/x

1 = 40/x

x = 40

As the distance between the walls is the sum of the bases of the triangles, 40 + 30 = 70 m

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

In ΔCAE

Perpendicular = CE = 40 m

Base = AE

∠CAE=30°

To find AE we will use trigonometric ratio

Thus the distance between walls = DA=DA+AE

=

=

Thus the distance between the two walls is 103.92 m

Hence Option C is correct.

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. The length of AB is 60m.AC is a ray of light which strikes the wall on the right at point C which is 40m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 45 degrees with the ground.

What is the distance between the walls?

80 m

140 m

70 m

110 m

Hence, the distance between two walls is:

100 m.

Step-by-step explanation:

We are asked to find the distance between the two balls.

This could be done if we first find the distance between the first wall and the laser bean=d

and then the second wall and the laser bean=d'

and then add both the distances to find the total distance between the two walls i.e. (d+d')

As the triangle is right triangle so we will use the trignometric identity to find the distance.

The distance between the first wall and laser beam is:

similarly The distance between the second wall and laser beam is:

Hence, the distance between the two walls is:

Hence, the distance between two walls is:

100 m.