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?

1) 173.20 m
2) 149.28 m
3) 103.92 m
4) 110.90 m

Answer 1

To find the distance between the walls, we can use trigonometry and the concept of similar triangles. The distance between the walls is approximately 173.20 meters.

Step-by-step explanation:

To find the distance between the walls, we can use trigonometry and the concept of similar triangles. Let's analyze the situation:

Angle A = 60 degrees

Angle B = 90 degrees (as the walls are perpendicular to the ground)

Angle C = 30 degrees

Height of point B = 60 meters

Height of point C = 40 meters

Using the tangent function, we can find the distance between the walls:

Tan(60 degrees) = height of point B / distance between walls

Tan(30 degrees) = height of point C / distance between walls

Simplifying the equations, we get:

Distance between walls = height of point B / tan(60 degrees) = height of point C / tan(30 degrees)

Plugging in the values, the distance between the walls is approximately 173.20 meters.