Robin hood plans to use a 54 ft ladder to reach the castle window of Maid Marian. Little John, who made the ladder, advised Robin that the angle of elevation of the ladder must be between \displaystyle 55^{of}55 o and \displaystyle 70^{of}70 o for safety. What are the minimum and maximum heights that can safely by reached by the top of the ladder when it is placed against the 50 ft castle wall

Answers

Answer 1

Answer:

The minimum height is: 44.24 ft and the maximum is 50.74ft

Step-by-step explanation:

Given

[tex]L = 54[/tex] --- Length of ladder

[tex]55 \le \theta \le 70[/tex]

Required

The minimum and maximum height

The question is illustrated with the attached image:

The height h is calculated using:

[tex]\sin(\theta) = \frac{h}{54}[/tex] --- sine equation

When [tex]\theta = 55[/tex], we have:

[tex]\sin(55) = \frac{h}{54}[/tex]

Make h the subject

[tex]h = 54 * \sin(55)[/tex]

[tex]h = 54 * 0.8192[/tex]

[tex]h = 44.24ft[/tex]

When [tex]\theta = 70[/tex], we have

This gives:

[tex]\sin(70) = \frac{h}{54}[/tex]

Make h the subject

[tex]h = 54 * \sin(70)[/tex]

[tex]h = 54 * 0.9397[/tex]

[tex]h = 50.74ft[/tex]

The minimum height is: 44.24 ft and the maximum is 50.74ft

Robin Hood Plans To Use A 54 Ft Ladder To Reach The Castle Window Of Maid Marian. Little John, Who Made

Related Questions

a trapezoids longer base is 4 times its shorter base. If the trapezoid has an area of 80 cm squared and a height of 8cm has what is the length of each base ​

Answers

Long One is 16
Short One is 4!!

A=base+base/2 * height

A=80

16+4/2 = 10

10 * 8 = 80!!

Black Wall Street: How did it end?​

Answers

Answer:

As news of these deaths spread throughout the city, mob violence exploded. White rioters rampaged through the black neighborhood that night and morning killing men and burning and looting stores and homes. Around noon on June 1, the Oklahoma National Guard imposed martial law, effectively ending the massacre.

I no knowww i no knowwwwww

Asked has saved $27 in bills to buy a bicycle helmet. Which set of bills represent the $27 Aksel has saved?

Answers

Answer:

A $20

A $5

And 2 ones.

add them up it =27

Step-by-step explanation:

HELP PLEASE DUE IN 4 MINUTES

Answers

It’s 1 ()(‘GF ykyxmhxmhmxmhdmydkyxk)
^ that’s to match the character limit

Pls pls pls pls help me

Answers

Answer:

m angle BCA =48 degrees

m angle ABC =70 degrees

m angle BAC=62 degrees

m angle BCD=132 degrees

Step-by-step explanation:

First you know that both interior angles have to equal the exterior angles (sorry I forgot what the name of the property). This means that the equation will be 6x-8+4x+10=12x-24. Simplify this to get 10x-2=12x-24. Simplify again to get 2x=26. Divide each side by 2 to get x=13. Now that you know x is equal to 13, you should plug x into angle ABC, BAC, and BCD. When you finish, angle ABC should be 70 degrees, angle BAC should be 62, and BCD should be 132.  To find angle BCA, you know that angle ABC is 70 degrees and BAC is 62 degrees. Every triangle has to equal 180 degrees so the equation should be 180-70-62 which is equal to 48. Therefore, m angle BCA =48 degrees, m angle ABC =70 degrees, m angle BAC=62 degrees, and m angle BCD=132 degrees. With this you can mark the correct choices.

Hope this helps you

A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz. Determine three sigma control limits for an x-bar (mean) chart assuming a sample size of 10. Group of answer choices UCL

Answers

Answer:

Upper Control Limit = 6.03 oz

Lower Control Limit = 5.97 oz

Step-by-step explanation:

Given - A process that makes chocolate candy bars has an output that is normally distributed with a mean of 6 oz. and a standard deviation of .01 oz.

To find - Determine three sigma control limits for an x-bar (mean) chart assuming a sample size of 10.

Proof -

Given that,

μ = 6

σ = 0.01

Z value for 3 sigma process = 3

Now,

Control limits are - μ ± Zσ

Now,

Upper Control limit (UCL) = μ + Zσ

And

Lower Control limit (LCL) = μ - Zσ

Now,

UCL = 6 + 3( 0.01 )

        = 6 + 0.03

       = 6.03

⇒UCL =6.03 oz

Now,

LCL = 6 - 3( 0.01)

      = 6 - (0.03)

      = 6 - 0.03

      = 5.97

⇒LCL =5.97 oz

∴ we get

Upper Control Limit = 6.03 oz

Lower Control Limit = 5.97 oz

In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=38°, and RS = 1.2 feet. Find the length of QR to the nearest tenth of a foot.

Answers

Answer:

1.9

Step-by-step explanation:

SOLVE FOR X TO THE NEAREST TENTH

Answers

Answer:

x = 8.8

Step-by-step explanation:

First, you have to solve the side length for the smaller triangle.

[tex]c= \sqrt{ a^{2} +b^{2} }\\c= \sqrt{5^{2}+4^{2} } \\\\c=\sqrt{25+16} \\c=\sqrt{41} \\c= 6.4\\[/tex]

Now for the bigger square.

[tex]c= \sqrt{ a^{2} +b^{2} \\} \\c = \sqrt{6.4^{2} +6^{2} } \\c= \sqrt{40.96+36} \\c= \sqrt{ 76.96}\\c= 8.77\\[/tex]

Rounded to the nearest tenth = 8.8

https://g.co/kgs/dg245M

I use this for my pythagorean theorem questions

Complete the table and fill in the last

Answers

Answer:

Its will be 2/3

Step-by-step explanation:

hope it helps you

Answer:

3/5…...........….........


Evaluate the function for the given value.
f(x) = 6for x = 4
f(4)=

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Don’t open that link they take all your information

How many is :
|-7 - 7|

Answers

Answer:

That is 14 I think

Step-by-step explanation:

Remove all signs when finding the absolute value.

A coin and a die are tossed. What is the probability of getting a 6 and a tail?​

Answers

Answer:

The probabilty is 1/2 for the coin and the probability is 1/6 for the die.

Hope this helps!

Step-by-step explanation:

Answer:

the posibility of getting a six on a die is 21/1 because there is 21 dot's on a die and getting a is 1/1 because there is only 2 sides hope this helps :)

Step-by-step explanation:

-x+y=1
-6x+3y=-12
Solve

Answers

Answer:

-x = -y + 1

x = 0.5y + 2

Step-by-step explanation:

If I save 20$ at the end of every month for 12 years, how much will I have?

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Answer:

2880

Step-by-step explanation:

144 months times 20 equals 2880

2 to the power of -5 as a product?

Answers

Answer:

1/32

Step-by-step explanation:

Answer:

0.03125

Step-by-step explanation:

2^(-5)

0.03125


Which of the following fractions are between 3/7 and 4/7?

Answers

3.5/7 is the answer to your question

Answer:

3.1-3.9/7 can be the answer.

Step-by-step explanation:

this is because you asked between and not exactly in half. 3.5/7 would be halfway

There are 3,848 students and staff at happy town high school. if the principal friendly and 15 teachers are infected by a zombie at the very beginning of a school day, and the rate of infection is that the number of zombies doubles every hour. would every student and staff member be infected before the 8 hour school day is over? why?

If you could please explain your answer. thank you very much.

Answers

Answer:

no

Step-by-step explanation:

at firth hr - 15×2=

2 nd hr - 60×2

and so on,it takes more than 8 hr

PLZ ANSWER I REALLY REALLY NEED IT

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D i think it’s d best answer

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Answers

Answer:

y=2x-1

Step-by-step explanation:

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Answer:

-2/2

Step-by-step explanation:

function calculator

will someone please help me? I will give 20 points!

Answers

Answer:

SA = 270 ft²

Step-by-step explanation:

SA = 2(12×5)/2 + (7×5) + (13×7) + (12×7)

SA = (12×5) + (7×5) + (13×7) + (12×7)

SA = 60 + 35 + 91 + 84

SA = 270 ft²

which of the following describes the roots of the polynomial function f(x)=(x-3)^4(x+6)^2

Answers

Answer:y=3x+4

Step-by-step explanation:

Answer:

3 with multiplicity 4 and 6 with multiplicity 2

Step-by-step explanation:

D

I need help figuring out the answers

Answers

Wait so do you need help or me to check them?

Part B Walden poses the same question (How many people live in your home, including yourself?) to each person in the house next to his. Based on their responses, he wrote this data set: 5, 5, 5, 5, 5. Question 1 What is the center of this data set?


PLZ answer the question

Answers

Answer:

The answer is 5

Step-by-step explanation:

get to the middle of the 5's and that's your answer =>=

Answer:

The answer is 5

Step-by-step explanation:

The net of a triangular prism is shown.
14 cm
5 cm
5 cm
6 cm
3 cm
What is the surface area of the prism?
O A. 46 cm
OD. 72 cm
O B. 54 cm
O E. 96 cm
OC. 69 cm

Answers

The answer is 14 and 46cm

sinificidigijilisidifigihijikopl

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Answer:

jhadfiogdivbdui

Step-by-step explanation:

The field where Marisol plays soccer is a rectangle 100 yards long and 60 yards wide. What is the perimeter of the soccer field?​

Answers

100x600=60000..............................

Answer:

320 yards long

Step-by-step explanation:

(100x2) + (60x2) = P

P = 200 + 120

P = 320 yards.

5 A box of donuts holds
12 donuts. One-fourth
of the donuts have
sprinkles. Of the remaining
donuts, one-third have
cherry filling. The rest are
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donuts are plain?

Answers

Answer:

91.6667%

Step-by-step explanation:

1/3 of 1/4 = 1/12

11/12 = 91.6667%

Have a great day <3

Answer:

50% of the donuts are plain

Step-by-step explanation:

out of 12 donuts, 1/4 have sprinkles. This results in 3 donuts having sprinkles. 3 out of 12 is 9. 1/3 of 9 is 3. 3 donuts have cherry filling. The rest, which is 6 are plain. 6 is 50% of 12.

From among the 300 largest cities in the United States, the FleeceU Auto Insurance Company identified the 10 safest and 10 least-safe U.S. cities based on the mean number of years drivers went between automobile accidents. The cities on both lists were the smaller cities on the list of the 300 largest.

Required:
Use facts about the sampling distribution model of the sample mean to explains why this is not surprising?

Answers

Answer:

7

Step-by-step explanation:

I just want points

Cities in which the mean is based on a smaller number of drivers will have greater variation in their means and are therefore more likely to be both safest and least safe.

What is random sampling?

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Given that, from among the 300 largest cities in the United States, the FleeceU Auto Insurance Company identified the 10 safest and 10 least-safe U.S. cities.

It is noted that mean is used to measure the safety of a city. It is known that outliers have more effect on the mean value. The outlier drags the center or mean value toward it. Also, small samples usually have more variation. This could be the reason why small cities are on both safe and least safe cities lists.

So, the correct option is d.

Options (a) and (c) do not include any interpretation in terms of mean. Option (b) suggests that data is bimodal, but it does not signify why small cities are more in the lists. Option (e) does not conclude in terms of mean. Option (f) suggests the phenomenon of traffic congestion in big cities, but it cannot be considered only because of traffic the mean year is less. Option (g) does not imply statistically meaningful evidence to suggest the claim. And, option (h) is almost the same as option (d). However, since it does not suggest more about the variation, it is incorrect. Thus, except option (d), the remaining all statements are not recommended.

Therefore, option D is the correct answer

Learn more about the random sample here:

https://brainly.com/question/12719656.

#SPJ6

"Your question is incomplete, probably the complete question/missing part is:"

From among the 300 largest cities in the United States, FleeceU Insurance Company identified the 10 safest and 10 least-safe U.S. cities based on the mean number of years drivers went between automobile accidents. The cities on both lists were the smaller cities on the list of the 300 largest. Use facts about the sampling distribution model of the sample mean to select the choice below that explains why this is not surprising.

a. More people in larger cities drive older cars that are more accident prone.

b. In smaller cities, the distribution of the mean number of years drivers go between accidents is bimodal, which makes it more likely they will be in the safest and least-safe cities.

c. Larger cities have a higher incidence of hit-and-run accidents.

d.Cities in which the mean is based on a smaller number of drivers will have greater variation in their means and are therefore more likely to be both safest and least safe.

e. Accident statistics are more accurate in smaller cities.

f. Traffic congestion in larger cities decreases the mean number of years drivers go between accidents but not enough to place larger cities In the least-safe group.

g.Large cities are not on the safest list because their mean time between accidents is reduced by people who "stage" accidents for purposes of insurance fraud.

h.Smaller cities are safer, but a few accident-prone drivers (outliers) in some small cities decreases the mean number of years between accidents, resulting in these cities being listed on the least-safe list.

Hi I need helpppp plzzzzzzzzzzzzsssss

Answers

Answer:

Step-by-step explanation:

Answer:

2, 8 and 14

is this for the subject math

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