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 60m.AC is a ray of light which strikes the wall on the right at point C which is 40m 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?

Answer 1

Answer: 70  meters.

Step-by-step explanation:

Observe the figure attached.

The distance between the walls is:

$DE=AD+AE$

Both triangles are right triangles. Therefore, you can calculate the distance  between the walls as following:

- Calculate the distance AD:

$cos\alpha=\frac{adjacent}{hypotenuse}\\\\cos(60\°)=\frac{AD}{60}\\AD=30m$

- Calculate the distance AE:

$tan\beta =\frac{opposite}{adjacent}\\\\tan(45\°)=\frac{40}{AE}\\\\AE=\frac{40}{tan(45\°)}\\\\AE=40m$

Therefore the distance between the walls is:

$DE=30m+40m=70m$

Answer 2

Answer:

70 m

Step-by-step explanation:

i took the test :)