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:

Answer 1

Answer:

100 m

Explanation:

To find the distance between the walls, we will find the distance from each wall to the laser source.

The distance of the first wall to the laser source is calculated as

$\begin{gathered} \cos60=\frac{\text{ Adjacent side}}{\text{ hypotenuse}} \\ \\ \cos60=\frac{\text{ x}}{40} \end{gathered}$

Where x is the distance from the first wall to the source. Then, the distance is equal to:

$\begin{gathered} 40\cdot\cos60=x \\ 40\cdot0.5=x \\ 20=x \end{gathered}$

On the other hand, the distance from the laser to the second wall is calculated as

$\begin{gathered} \tan45=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \\ \tan45=\frac{80}{y} \end{gathered}$

Where y is the distance from the second wall to the laser. Solving for y, we get

$\begin{gathered} y\cdot\tan45=80 \\ \\ y=\frac{80}{\tan45} \\ \\ y=\frac{80}{1} \\ \\ y=80 \end{gathered}$

Then, the distance from wall to wall is equal to

x + y = 20 + 80 = 100

Therefore, the answer is 100 m