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Novay_Z [31]
3 years ago
10

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 an

d 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 30 meters above the ground. AC is a ray of light which strikes the wall on the right at point C. The length of AC is 80 meters. The ray AB makes an angle of 45 degrees with the ground. The ray AC makes an angle of 60 degrees with the ground.

What is the distance between the walls?

Mathematics
1 answer:
Nataly [62]3 years ago
4 0

Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

\tan\theta=\frac{perpendicular}{base}

Here \theta=45^{\circ} , perpendicular = 30 m  and base we can find.

thus,

\tan 45^{\circ}=\frac{30}{EA}

We know \tan 45^{\circ}=1

thus, EA =  30 m

Consider the Δ AEB,

Using trigonometric ratio,

\cos\theta=\frac{base}{hypotenuse}

Here \theta=60^{\circ} , hypotenuse = 80 m  and base we can find.

thus, \cos 60^{\circ}=\frac{base}{80}

We know, \cos 60^{\circ}=\frac{1}{2}

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

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3 years ago
(CO 4) In a sample of 8 high school students, they spent an average of 24.8 hours each week doing sports with a sample standard
AveGali [126]

Answer:  

(22.12, 27.48)

Step-by-step explanation:

Given : Significance level : \alpha: 1-0.95=0.05

Sample size : n= 8 , which is a small sample (n<30), so we use t-test.

Critical values using t-distribution: t_{n-1,\alpha/2}=t_{7,0.025}=2.365

Sample mean : \overline{x}=24.8\text{ hours}

Standard deviation : \sigma=3.2\text{ hours}

The confidence interval for population means is given by :-

\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}

i.e. 24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}

24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)

Hence, the 95% confidence interval, assuming the times are normally distributed.=  (22.12, 27.48)

6 0
3 years ago
The exponential model A = 661.7 e^0.011t describes the population, A, of a country in millions, t years after 2003. Use the mode
faust18 [17]

Answer:

661.7 million

Step-by-step explanation:

Given the exponential model :

A = 661.7 e^0.011t

The general form of an Exponential model is expresses as :

A = A0 * e^rt

Where A = final value ; A0 = Initial value ; r = growth rate and t = time elapsed

From the question t = time after 2003

Therefore, A0 = initial population, which is the population in 2003

Therefore, A0 = 661.7

Or we could put t = 0 in the equation and solve for A

A = 661.7 e^0.011(0)

A = 661.7 * 1

A = 661.7

Hence, population in 2003 is 661.7 million

7 0
3 years ago
The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, wh
Over [174]
<span>11.5 Not sure but it should be the answer!!

</span>
4 0
3 years ago
Read 2 more answers
Helppppppp plssssssssss no unhelpful answer or I will delete
lara31 [8.8K]

Answer:

80 sq.in

Step-by-step explanation:

One square's side = 4in

One square's area = 16 sq. in

16 x 5 = 80 sq.in

Hope that helps!

3 0
2 years ago
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