Mathematics, 19.07.2019 14:00 chelton3813

Asource 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

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Answer from: itsdeevv

Let

be the distance from the left wall to the laser source and

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

:
$cos( \alpha )= \frac{adjacent.side}{hypotenuse}$
$cos(60)= \frac{x}{40}$
x=40cos(60)

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

:
$tan( \alpha )= \frac{opposite.side}{adjacent.side}$
$tan(45)= \frac{80}{y}$
$y= \frac{80}{tan(45)}$
y=80m

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

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

Asource of laser light sends rays ab and ac toward two opposite walls of a hall. the light rays stri

Asource of laser light sends rays ab and ac toward two opposite walls of a hall. the light rays stri

Answer from: cindyramirez3140

The distance between the walls is 100 m and this can be determined by using the trigonometric function.

Given :

A source of laser light sends rays AB and AC toward two opposite walls of a hall.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.The length of AB is 40m. AC is a ray of light that 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.

Let the distance between the left wall and the laser source be 'x' and the distance between the right wall and the laser source be 'y'.

Now, apply trigonometric function in order to determine the value of 'x'.

$\rm cos \;60=\dfrac{x}{40}$

0.5 $\times$ 40 = x

x = 20 m

Again apply trigonometric function in order to determine the value of 'y'.

$\rm tan\; 45=\dfrac{80}{y}$

y = 80

So, the distance between the walls is given by:

x + y = 80 + 20 = 100 m

For more information, refer to the link given below:

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Answer from: Quest

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Answer from: Quest

step-by-step explanation:

a and d

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