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: what is the distance between the walls? (1 point)

Explanation:

Step1: Find distance from A to left wall

Let $x$ = distance from A to left wall. In the 45° right triangle, $\tan(45^\circ)=\frac{30}{x}$. Since $\tan(45^\circ)=1$,
$x = \frac{30}{\tan(45^\circ)} = 30$ m

Step2: Find distance from A to right wall

Let $y$ = distance from A to right wall. In the 60° right triangle, $\cos(60^\circ)=\frac{y}{80}$. Since $\cos(60^\circ)=0.5$,
$y = 80 \times \cos(60^\circ) = 80 \times 0.5 = 40$ m

Step3: Calculate total wall distance

Add the two distances:
Total distance = $x + y$

Answer:

$30 + 40 = 70$ m