Looking north, two skyscrapers are sighted from the viewing deck of the Empire State Building at 1250 feet up. One skyscraper is sighted at a 20° angle of depression and a second skyscraper is sighted at a 30° angle of depression. How far apart are the two skyscrapers to the nearest foot?

Answers

Answer 1

Answer:

Step-by-step explanation:

Looking North, Two Skyscrapers Are Sighted From The Viewing Deck Of The Empire State Building At 1250
Answer 2

The angle of depression is the angle between the line of sight and a vertical line.

The distance between the two skyscrapers is 1269ft

I've added as an attachment, a figure that illustrates the scenario

First, we calculate distance AB using the following tangent ratio

[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{\tan(60) = \frac{AB}{1250}}[/tex]

Make AB the subject

[tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]

Next, we calculate distance AC using the following tangent ratio

[tex]\mathbf{\tan(\theta) = \frac{Opposite}{Adjacent}}[/tex]

So, we have:

[tex]\mathbf{\tan(60+10) = \frac{AB + BC}{1250}}[/tex]

[tex]\mathbf{\tan(70) = \frac{AB + BC}{1250}}[/tex]

Make AB + BC, the subject

[tex]\mathbf{AB + BC = 1250 \times \tan(70)}[/tex]

Make BC the subject

[tex]\mathbf{BC = 1250 \times \tan(70) - AB}[/tex]

Substitute [tex]\mathbf{AB = 1250 \times \tan(60)}[/tex]

[tex]\mathbf{BC = 1250 \times \tan(70) - 1250 \times \tan(60)}[/tex]

[tex]\mathbf{BC = 1269}[/tex]

Hence, the distance between the two skyscrapers is 1269ft

Read more about angles of depression at:

https://brainly.com/question/13697260

Looking North, Two Skyscrapers Are Sighted From The Viewing Deck Of The Empire State Building At 1250

Related Questions

Someone help me PLZZ

Answers

Answer:

5/3

Step-by-step explanation:

The slope is the coefficient next to the x. Therefore, the slope is 5/3.

Answer:

m= 5/3

Step-by-step explanation:

Math wizzz

Worked it out

And online calculator verified!

Please help I need to get this done and I have no idea what I'm doing!

Answers

Answer:

5

Step-by-step explanation:

(125) ^ (1/3)

We can rewrite 125 as 5^3

( 5^3) ^ 1/3

We know that a^b^c =a ^ (b*c)

5 ^(3*1/3)

5^ 1

5

Answer:

5

Step-by-step explanation:

when something is to the power of 1/2, that means you square root it

when it is to the power of a third, that means you cube root it.

for example, if it is 25 to the power of a half, that means [tex]\sqrt{25} = 5[/tex] because

5 x 5 = 25

this is the same concept

we need to find a number that multiplies itself 3 times and equals to 125

5x5x5 = 125, meaning that

125 to the power of a third, is 5.

i need help asap please

Answers

8x^2y is correct
Hope this helps

Yesterday movie theaters sold 261 bags of popcorn a large bag of popcorn cost three dollars a small bag of popcorn cost one dollar in all the movie theater made $443 from popcorn sales right and solve a system of equations to find how many bags of each size of popcorn were sold

Answers

kannaoakaksmsamammamsmma 66

how many oz are in 1 gallon and a cup​

Answers

72038302229877777389Step-by-step explanation:

A test of a new car results in 370 miles on 10 gallons of gas. How far could you drive on 65 gallons of gas?
Show your work

Answers

Answer:

2405 miles

Step-by-step explanation:

370÷10 = 37

37×65 = 2405

33333333333333333333333333333

Answers

Answer: All three methods would be easy and effective

Step-by-step explanation:  

What is the slope of the line in this graph?

Answers

Answer:

90% sure it's 5/7

Step-by-step explanation:

PLEASE HELP ASAP!! DUE TODAY

Answers

Answer:

Step-by-step explanation:

when  1/2 inch equals 4 feet the room is  2.25 inches, then

2 1/4 = 8/4 + 1/4  = 9/4

9/4 inches is the scale distance of the room

each 1/2 inch is 4 feet so divide  9/4 by 1/2 then multiply that by 4 to find the distance of the room

9/4 ÷ 1/2  = 9/4

9/4 * 2/1 = 18/4

18/4 = 9/2

9/2 * 4 feet = 9/2 * 4/1

9/2 * 4/1 = 36/2

36/2=18

the room is 18 feet across

then if the scale is 2/3 of an inch is  4 feet , then

2/3 * 9/4 = 18/12

18/12 = 3 inches  is the scale size of Quinto's room

33 m
44 m
What is the length of the hypotenuse?
C=
meters

Answers

Answer:

3

Step-by-step explanation:

Use the reverse form of the pythagorean theorem.

c^2 - b^2 = a^2

25 - 16 = 9

square root of 9 is 3

pls answer my question please correctly

Answers

Answer:

13/10 5/3 40-78 C A

Step-by-step explanation:

PLEASE HELP ASAP! DO IN 5 MINUTES! WILL MARK BRAINLIEST!!!!!!

Answers

Answer:

Step-by-step explanation:

cos²(x) = 1-sin²(x) = 144/169

cos(x) = √(144/169) = 12/13

:::::

tan(x) = sin(x)/cos(x) = (5/13)/(12/13) = (5/13)×(13/12) = 5/12


Order the ANGLES in each triangle from SMALLEST to largest.

Answers

Answer:

S,R,Q

Step-by-step explanation:

Pls help me i don’t know what to do

Answers

Answer and Step-by-step explanation:

The answer that we have agreed upon is answer choice 2, C, A, B.

This is because the first distance is found, and could possibly be the hypotenuse, noted as C, then the other two sides are created, becoming the legs of a triangle, noted as A and B respectively.

I hope this helps and is correct!

#teamtrees #PAW (Plant And Water)

Hi I need help please ASAP

Answers

Get photomath or Symbolab!!!

Calculate 18% tip on a 6250 dinner bill

Answers

The 18% tip would be 1,125 therefore, leading the total to be 5125. :)


A line passes through the point (4, -2) and has a slope of -5/4
Write an equation in slope-intercept form for this line.

Answers

Answer:

ftudhdldkdjfjdn cbgffrwwof

Lee wants to buy four tee shirts,
which were originally priced $12.94
each. He purchases four shirts at the
"Buy One Get One 50%" sale and pays
6.2% tax on the total cost of the
shirts. Including the tax, what will be
the cost of each shirt?

Answers

Answer:

$27.48

Step-by-step explanation:

He buys 1 shirt at 12.94 and gets one at 6.47

He does this 2 times and the total is 25.88

That times 1.062 to factor in the 6.2 percent tax rate is 27.48

So first you do:

.5 x 12.94=6.47

Next:

6.47 x 2=12.94

Then:

12.94 x 3=38.82

Now you have to do the tax:

38.82 x .062=2.41

After you get the answer for tax you have to add that to the price with out tax:

So, 38.82+2.41

=41.23

So you answer is 41.23 including the discount and tax

-24 = x - ( - 2

need help please​

Answers

Answer:

okay here is the answer but no work shown

x= -16

i got -26 but i’m not sure if it’s correct

How much more than the original $10,000 do you pay in interest?

Answers

Answer:

In a savings account earning 0.01%, your balance after a year would be $10,001.

Step-by-step explanation:

-4w - 3( -9 + 5w) Combine Like Terms Using the Distributive Property

Answers

Answer: =−19w+27

Step-by-step explanation:Hope this help :D

Please solve this and give answer

Answers

Answer:

Step-by-step explanation:

In a bag, Bag C, the ratio of red counters to yellow counters is 3 : 4.
If 3 of the red counters are removed from Bag C, the ratio of red counters
to yellow counters is 3 : 5.

How many yellow counters are in Bag C?

Answers

Answer:

20

Step-by-step explanation:

The ratio of red : yellow is 3 : 4 = 3x : 4x ( x is a multiplier )

If 3 red counters are removed then

red : yellow = 3x - 3 : 4x = 3 : 5

Expressing in fractional form

[tex]\frac{3x-3}{4x}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5(3x - 3) = 12x

15x - 15 = 12x ( subtract 12x from both sides )

3x - 15 = 0 ( add 15 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

number of yellow counters = 4x = 4 × 5 = 20

HELPPPPP PLSSSSSSSSSWSSSS

Answers

Answer:

D.

Hope that helps!

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Hope this helps

Given the first term and the common ratio of a geometric
sequence find the first five terms and the explicit formula. a1
= 0.8, r= −5

Answers

Answer:

nth term = 0.8 * -5^(n - 1)

First five terms are: 0.8, -4,

20, -100, 500

Step-by-step explanation:

First term, a1 = 0.8

Common ratio, r = -5

a1 = 0.8

Second term = ar

= 0.8 * -5

= -4

Third term = ar²

= 0.8 * -5²

= 0.8 * 25

= 20

Fourth term = ar³

= 0.8 * -5³

= 0.8 * -125

= -100

Fifth term = ar⁴

= 0.8 * -5⁴

= 0.8 * 625

= 500

First five terms are: 0.8, -4,

20, -100, 500

nth term = ar^(n - 1)

= 0.8 * -5^(n - 1)

nth term = 0.8 * -5^(n - 1)

does anyone know this i will give brainliest

Answers

Answer: -324.4

Step-by-step explanation:

what is the volume of the cube if one side is equal to 6 cm

Answers

Answer:

The volume is 216 cm³

Step-by-step explanation:

Hope this helped Mark BRAINLEST!!!

someone please help me with this problem

Answers

Answer:

x=45

y=135

z=45

What is 7/10 of 650?

Answers

Answer:

455

Step-by-step explanation:

I answered first, but forgot to answer here.

Can anybody help me with these, they're awfully confusing.

Answers

Answer:

20) a) 6.8 b) 7

21) a) 26.2 b) 26

22) a) -7.8 b) -8

23) a) -10.2 b) -10

24) a) 2.6 b) 3

25) a) -12.9 b) -13

9) Real number

10) Real number

11) Real number

12) Real number

13) Real number

14) Real number

15) Not a real number

16) Real number

Explanation

In order to find the estimated integer of a square root, you simply find the perfect squares closest to the specified square root. For example, the closest perfect squares to [tex]\sqrt{46}[/tex] are [tex]\sqrt{36}[/tex] and [tex]\sqrt{49}[/tex]. Now, we need to find which perfect square is the closest between those two. 46 and 36 have a difference of 10, while 46 and 49 have a difference of 3. So, we know that 49 is the closest perfect square. Now, we simplify

Other Questions
If M= {m, a,t} how many subsets of M are there? Help, please I really want to get a good grade Dickon and the robin like Mary.Question 4 options: True False How might a community's geographic location impact its decision to be imperialist or isolationist? find the perimeter and area. round to the nearest whole number if needed. 9. How did Jeroboam lead his people away from God? An automobile of mass 1.46 E3 kg rounds a curve of radius 25.0 m with a velocity of 15.0 m/s. Thecentripetal force exerted on the automobile while rounding the curve is: SOMEONE PLEASE HELP METhe average kinetic energy of the particles of two pieces of iron at the same temperature and mass would be __________.Question 1 options:DifferentThe sameNot equivilentWith in 500 degrees of eachother Floyd Electric is fabricating flanges for a new electrical motor. The flange is to be 25 millimeters in diameter with an upper tolerance limit of 26.5 millimeters and a lower tolerance limit of 23.5 millimeters. Bill Floyd took a sample consisting of ten flanges, measured the diameter and recorded the observations in the table. He has heard discussion of 6 sigma in the business news recently and would like to join the club. What percentage decrease in process standard deviation would be required for Floyd Electric to achieve 6-sigma process capability? Assume that his process mean remains where it is. A) 36% B) 40% C) 46% D) 58% cause and effect concave lenses side of lenses are curved inward Huck, I need help, and I don't get help, I'll Ducking do it again A boat can travel 128.8 miles on 16.1 gallons of gasoline. How far can it travel on 9.4 gallons? A bank account pays 0.5% monthly interest. If $500 is put in the account, what will the balance be at the end of one year, assuming no additional deposits or withdrawals are made? Do not include units ($) in your answer. All of the organisms in the domain Archaea areA. prokaryotesB. eukaryotesC. autotrophsD. multicellular Write a SELECT statement that answers this question: Which products have a list price thats greater than the average list price for all products? Write this using a subquery. Return the ProductName and ListPrice columns for each product. Sort the results by the ListPrice column in descending sequence. Match each type of persuasive message to its example.proposalrequestclaim A group of statisticians at a local college has asked you to create a set of functions that compute the median and mode of a set of numbers. Define these functions, median and mode, in a module named stats.py. Also include a function named mean, which computes the average of a set of numbers. Each function should expect a list of numbers as an argument and return a single number. Each function should return 0 if the list is empty. Include a main function that tests the three statistical functions using the following list defined in main:List: [3, 1, 7, 1, 4, 10]Mode: 1Median: 3.5Mean: 4.33333333333#Here is the code I am using:def median(list):if len(list) == 0:return 0list.sort()midIndex = len(list) / 2if len(list) % 2 == 1:return list[midIndex]else:return (list[midIndex] + list[midIndex - 1]) / 2def mean(list):if len(list) == 0:return 0list.sort()total = 0for number in list:total += numberreturn total / len(list)def mode(list):numberDictionary = {}for digit in list:number = numberDictionary.get(digit, None)if number == None:numberDictionary[digit] = 1else:numberDictionary[digit] = number + 1maxValue = max(numberDictionary.values())modeList = []for key in numberDictionary:if numberDictionary[key] == maxValue:modeList.append(key)return modeListdef main():print ("Mean of [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]: "), mean(range(1, 11))print ("Mode of [1, 1, 1, 1, 4, 4]:"), mode([1, 1, 1, 1, 4, 4])print ("Median of [1, 2, 3, 4]:"), median([1, 2, 3, 4])main()The Error that I am getting is on Line 14: AttributeError: 'range'object has no attribute 'sort'.Also on Line 36:Line36: 10]: "), mean(range1, 11)). IIInitial Knowledge CheckA circle has a diameter of 32 mm. What is its circumference?Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.2mm32 mm5Marking Brainlyest the sum of the ages of tracy and her mother is 60 if tracys present age is y years write a linear expression for her mothers age after 5 years the average mark of three pupils are 68. what is the ratio of 5:4:3. how many marks did the best student get? HELP ME!