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 which is 60 meters above the ground. AC is a ray of light which strikes the wall on the right at point C which is 40 m above the ground. The ray AB makes an angle of 60 degrees with the ground. The ray AC makes an angle of 30 degrees with the ground. What is the distance between the walls?

Answer 1

There are several ways to solve this problem. The easiest one is by trigonometry. I am going to apply this method. If you didn't see trigo yet, I will use the triangles semi equilateral.
Let BD, be the wall on the left and CE on the right (B and D = base of the wall)

1) In Δ BAD, angle BAD = 60°→→ tan (60) =(opposite side)'(adjacent) =BD/DA

tan (60) = 60/DA , but tan (60) = √3 →→√3 = 60/DA or DA = 60/√3

And DA = 34.64

2) In Δ ACE, angle CAE = 30°→→ tan (30) =(opposite side)'(adjacent) =EC/AE

tan (30) = 40/AE , but tan (30) = √3/3 →→√3/3 = 40/AE or AE = (40)/(√3/3)

And AE = 68.28

3) Distance between walls = DA + AE = 34.64 + 68.28 = 103.92
(If you didn't study trigo yet, do let me know then we will solve it with the semi equilateral triangles

Answer 2

The distance between the walls is $60\sqrt3$ meters.

Given information:

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.

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 60 m above the ground.
• AC is a ray of light that strikes the wall on the right at point C which is 40 m above the ground.
• The ray AB makes an angle of 60 degrees with the ground and the ray AC makes an angle of 30 degrees with the ground.

Let the distance between source A and left wall is x, and that between source A and right wall is y.

Use the trigonometric ratios to find the distance between the walls as,

$tan60=\dfrac{60}{x}\\\sqrt3=\dfrac{60}{x}\\x=20\sqrt3\\tan30=\dfrac{40}{y}\\\dfrac{1}{\sqrt3}=\dfrac{40}{y}\\y=40\sqrt3$

So, the distance between the walls will be,

$x+y=20\sqrt3+40\sqrt3\\x+y=60\sqrt3$

Therefore, the distance between the walls is $60\sqrt3$ meters.

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https://brainly.com/question/14983337