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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: What is the distance between the walls? 30 m 40 m 70 m 100 m

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 What Is The Di class=

Sagot :

In order to calculate the distance between the walls, let's use the tangent relation of angle 45° and the cosine relation of angle 60°.

The tangent is equal to the opposite leg over the adjacent leg, and the cosine is equal to the adjacent leg over the hypotenuse.

So we have:

[tex]\begin{gathered} \tan45°=\frac{40}{x}\\ \\ 1=\frac{40}{x}\\ \\ x=40\text{ m}\\ \\ \\ \\ \cos60°=\frac{y}{60}\\ \\ \frac{1}{2}=\frac{y}{60}\\ \\ 2y=60\\ \\ y=30\text{ m} \end{gathered}[/tex]

Now, adding the values of x and y (which are the distances from each wall to the laser source), we have the distance between the walls:

[tex]d=x+y=40+30=70\text{ m}[/tex]

Correct option: third one.

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