4) The path of a satellite orbiting the earth causes it to pass directly over two
tracking stations A and B, which are 60 km apart. When the satellite is on one side of
the two stations, the angles of elevation at A and B are measured to be 86.4 ° and
85 °, respectively.
Find how far the satellite is from station A and how high the satellite is above the
ground. Round your answers to 2 decimal places.
Answers
Answers:
Satellite is approximately 2446.43 km from station A.Satellite is approximately 2441.61 km above the ground.=========================================================
Explanation:
I'm assuming tracking stations A and B are at the same elevation and are on flat ground. In reality, this is likely not the case; however, for the sake of simplicity, we'll assume this is the case.
The diagram is shown below. Points A and B describe the two stations, while point C is the satellite's location. Point D is on the ground directly below the satellite. We have these lengths
AB = 60 kmAD = xCD = hFocusing on triangle ACD, we can apply the tangent rule to isolate h.
tan(angle) = opposite/adjacent
tan(A) = CD/AD
tan(86.4) = h/x
x*tan(86.4) = h
h = x*tan(86.4)
We'll use this later in the substitution below.
--------------------
Now move onto triangle BCD. For the reference angle B = 85, we can use the tangent rule to say
tan(angle) = opposite/adjacent
tan(B) = CD/DB
tan(B) = CD/(DA+AB)
tan(85) = h/(x+60)
tan(85)*(x+60) = h
tan(85)*(x+60) = x*tan(86.4) ............. apply substitution; isolate x
x*tan(85)+60*tan(85) = x*tan(86.4)
60*tan(85) = x*tan(86.4)-x*tan(85)
60*tan(85) = x*(tan(86.4)-tan(85))
x*(tan(86.4)-tan(85)) = 60*tan(85)
x = 60*tan(85)/(tan(86.4)-tan(85))
x = 153.612786190499
--------------------
We'll use this approximate x value to find h
h = x*tan(86.4)
h = 153.612786190499*tan(86.4)
h = 2441.60531869599
h = 2441.61 km is how high the satellite is above the ground.
Return to triangle ACD. We'll use the cosine rule to determine the length of the hypotenuse AC
cos(angle) = adjacent/hypotenuse
cos(A) = AD/AC
cos(86.4) = x/AC
cos(86.4) = 153.612786190499/AC
AC*cos(86.4) = 153.612786190499
AC = 153.612786190499/cos(86.4)
AC = 2446.43279498247
AC = 2446.43 km is the distance from the satellite to station A.
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Answer:
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Step-by-step explanation:
Answer:
x = -3
Step-by-step explanation:
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[tex]\frac{1/8}{9}[/tex] is the answer.
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Answers
g’(x) = 12x^3 - 24x^2
Set equal to zero and solve:
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Given the function [tex]g (x) = 3x^4 - 8x^3[/tex]
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[tex]g'(x)= 12x^3-24x^2\\0= 12x^3-24x^2\\ 12x^3-24x^2=0\\12x^2(x-2)=0\\12x^2=0 \ and \ x - 2 = 0\\x = 0 \ and\ 2 \[/tex]
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Answers
Answer:
Step-by-step explanation:
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10. *
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Step-by-step explanation:
PLSSSSS
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1. Solve the system algebraically to determine the balance point between
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Answers
Answer:
Step-by-step explanation:
Subtract equation 2 from equation 1
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Answers
Answer:
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Step-by-step explanation:
If it's 18% for 9 months (and not per year)
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Answers
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Step-by-step explanation:
divide through by 9:
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Answer:
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Step-by-step explanation:
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[tex] \sqrt{16} [/tex]
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Step-by-step explanation:
Trust me it's right
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Answer:
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Step-by-step explanation:
The linear equations above match the lines in terms of slope and y-intercept.
I hope you found this helpful! If you did, I'd really appreciate if you'd mark my work as 'brainliest'. Please don't hesitate to ask any questions!
Have a great day!
The system of linear inequalities of the given points is required.
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[tex]x-3y\leq -9[/tex]
[tex]3x-y>2[/tex]
Points of the first line
[tex](0,3)[/tex]
[tex](3,4)[/tex]
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It is also a solid line.
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[tex](0,-2)[/tex]
[tex](1,1)[/tex]
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Let us take a point towards the right of the line [tex](2,2)[/tex]
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Step-by-step explanation:
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The question is unclear. Please provide the table.
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
perimeter=16+12+20
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Answer:
48
Step-by-step explanation:
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Answers
Answer:
5
Step-by-step explanation:
Given that:
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Answers
Answer:
28.26 cm²
Step-by-step explanation:
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Answers
Answer:
A: 8 x 10^6
Step-by-step explanation:
Please help!
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Answer:
The standard deviation is the best measurement of spread for games and movies.
help, please!!!its urgent
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Answer:
Step-by-step explanation:
its f because its pretty easy
Will mark brainliest! help asap! Don’t scam
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Mark's dad is three times older than Mark. Mark's sister is 2 years younger than Mark. (3m) The sum of their ages is 48. How old are Mark, his sister, and his dad?
Answers
Answer:
Age of Mark [tex]=10[/tex] years
Age of Mark's dad [tex]=30[/tex] years
Age of Mark's sister [tex]=8[/tex] years
Step-by-step explanation:
Let age of Mark be [tex]x[/tex] years.
Mark's dad is three times older than Mark
Age of her Mark's dad [tex]=3x[/tex]
Mark's sister is 2 years younger than Mark
Age of Mark's sister [tex]=(x-2)[/tex] years
The sum of their ages is 48.
[tex]x+3x+x-2=48\\5x-2=48\\5x=50\\x=10[/tex]
Age of Mark [tex]=x=10[/tex] years
Age of Mark's dad [tex]=3x=3(10)=30[/tex] years
Age of Mark's sister [tex]=x-2=10-2=8[/tex] years