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.

Answer 1

please do NOT just tell me the answer I want an explanation

Answer 2

What is the distance between the walls?

Answer 3

Let the remaining vertices of the triangles with vertex B and vertex C be given by D and E respectively:
Hence in triangle ABD, we have :
\[ \huge \cos \theta = \frac{DA}{AB} \rightarrow \cos 60^0 = \frac{DA}{40}\]
\[ \huge \rightarrow \frac{1}{2} = \frac{DA}{40} \rightarrow DA = 20 m\]
Next in triangle ACE, we have
\[\huge \tan \theta = \frac{CE}{AE} \rightarrow \tan 45^0 = \frac{80}{AE}\]
\[\huge \rightarrow 1 = \frac{80}{AE} \rightarrow AE = 80 m\]
Now distance between two walls = DA + AE = 20 + 80 = 100 m

@Sashamichelle

Answer 4

thanks so much!