Question

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 that strikes the wall on the left at point B, which is 30 meters above the ground. AC is a ray of light that strikes the wall on the right at point C. The length of AC is 80 meters. The ray AB makes an angle of 45 degrees with the ground. The ray AC makes an angle of 60 degrees with the ground.

Answer 1

Taking the right angle triangle formed on the left hand side, we have:

We will find the labelled side x, thus we have:

$\begin{gathered} \text{Tan 45=}\frac{30}{x} \\ 1=\frac{30}{x} \\ x=30m \end{gathered}$

Taking the triangle formed on the right hand side, we have:

We will find the labelled side y, thus we have:

$\begin{gathered} \cos \text{ 60=}\frac{y}{80} \\ 0.5=\frac{y}{80} \\ y=80\times0.5=40m \end{gathered}$

Hence, the distance between the two walls is 30m + 40m = 70m, which is option D