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. The length of AB is 40m. AC is a ray of light which strikes the wall on the right at point C which is 80 m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 45 degrees with the ground. What is the distance between the walls? 80 m 180 m 90 m 100 m

Answer 1

Let $x$ be the distance from the left wall to the laser source and $y$ the distance form the right wall to the laser source. 

We can use the cosine trigonometric function in the smaller triangle to relate the adjacent side of the angle and the hypotenuse; then we can solve for $x$:
$cos( \alpha )= \frac{adjacent.side}{hypotenuse}$
$cos(60)= \frac{x}{40}$
$x=40cos(60)$
$x=20m$

We can use the tangent trigonometric function in the larger triangle to relate the opposite side of the angle and its adjacent side; then we can solve for $y$:
$tan( \alpha )= \frac{opposite.side}{adjacent.side}$
$tan(45)= \frac{80}{y}$
$y= \frac{80}{tan(45)}$
$y=80m$

Now we can add both distances:
$20m+80m=100m$

We can conclude that the distance between the walls is 100 m.