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:

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

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136

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A pollster surveys 80 people to determine whether they will vote for Seth Gleason for mayor. 42 out of 80 say yes. What is the experimental probability that the next person surveyed will say he or she plans to vote for Seth Gleason?

Answers

Answer:

42 out of 80

Step-by-step explanation:

Given function:

surveys 80 people42 votedto find the experimental probability that the next person surveyed say yes or no..

Thinks:

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<

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Step-by-step explanation:

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Answers

3/12=1/4 or 25%. You can simply 3/12 by 3. 3/3=1 and 12/3=4, and therefore: 3/12=1/4.

I need help with this question it's for a important grade and if anyone can help that will be great.​

Answers

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Step-by-step explanation:

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Answers

Answer:120 meters

Step-by-step explanation:

8 × 15

Answer:

120 m

Step-by-step explanation:

Speed = 8 m/s

Distance traveled  in 1 sec = 8 m

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

13.2 miles

Step-by-step explanation:

To solve this, we will need to first solve for the base of the triangle and then use the information we find to solve for the shortest route.

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Answer:

x = 10

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Step-by-step explanation:

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Answers

Answer:

6

Step-by-step explanation:

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25-19=6

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Answer:

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Step-by-step explanation:

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Answer:

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Answers

No, Brianna is not correct.
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Step by step explanation:

1) Semi circle with a diameter equal to the side opposite it, 20 ft.
Find the length of half the circle:
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Circumference of semi-circle = (1/2)(3.14)(20 ft) = 31.4 ft.
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3.) Horizontal length at 20 ft.
Add the semi-circle, vertical, and horizontal lengths:
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Distance around the pool = 131.4 ft.

No, Brianna is not correct.

The distance around the pool is 131.4 ft

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P=(πr + 2r)

here, we have,

1) Semi circle with a diameter equal to the side opposite it, 20 ft.

Find the length of half the circle:

Circumference of semi-circle = (1/2)(πd)

Where:

π = 3.14

d = 20 ft.

Circumference of semi-circle = (1/2)(3.14)(20 ft) = 31.4 ft.

2) Vertical lengths from the endpoint of semi-circle to the endpoints of horizontal lengths, 40 ft each ⇒ 2 × 40 ft. = 80 ft.

3.) Horizontal length at 20 ft.

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Answer:

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The correct answer is c

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

x is b because 59 is less than 60 but greater than 57.

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c

Step-by-step explanation:

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Answers

Answer:

f(1)=10

Step-by-step explanation:

f(x)=9x+1

Substitute all values of x as 1

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I hope this helps!

Answer:

Step-by-step explanation:

Given

f(x) = 9x + 1f(1) = 9*1 + 1      = 9+1      =10hope it helps :)

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