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.
Related Questions
PLSSSSS
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Answers
Answer:
Step-by-step explanation:
Subtract equation 2 from equation 1
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2.2x=20
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Answer:
2x-2
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
which table of values can be defined by the function y =6x - 2?
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Step-by-step explanation:
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when ms mason bought a new computer she borrowed 1200 at the rate of 18% for 9 months how much interest did she pay
Answers
Answer:
$216 or $162 (see below)
Step-by-step explanation:
If it's 18% for 9 months (and not per year)
then
1200x0.18=$216
If it's 18% per year then
1200x0.18x0.75=$162
Will mark brainliest! help asap! Don’t scam
Answers
Tina likes to go on distance-learning steam she travels 60 K in 12 seconds what is the constant of proportionality
Answers
Answer:
5
Step-by-step explanation:
Given that:
60km in 12 seconds
Distance α time
Distance = k * time
K = constant of proportionality
Distance = 60 ; time = 12 seconds
60 = 12k
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What is the perimeter of this triangle?
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Answers
Answer:
Step-by-step explanation:
perimeter=16+12+20
= 48
Answer:
48
Step-by-step explanation:
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11
Mason throws a coin 3 times.
The outcome of each throw is either Heads or Tails.
List all the possible outcomes of the 3 throws.
w
Answers
HHH
HHT
HTT
HTH
TTT
TTH
THH
THT
Extra-large pizzas are on sale at a 15% discount. The original cost of an extra-large pizza is $28.00. How much is the cost of the pizza after the discount?
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Will give brainliest if correct!
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Answer:
m = 2
Step-by-step explanation:
Plug 2 coordinates into the slope formula
(y2-y1)/(x2-x1)
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Answers
Answer:
-3
Step-by-step explanation:
Answer:
x = -3
Step-by-step explanation:
This should be the answer. Brainliest would be appreciated.
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Answer:
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Hope this helped!
Step-by-step explanation:
Which table has a constant of proportionality between y and 2 of 0.3?
Choose 1 answer:
y
6
2
12
4
30 10
2
y
3 1.8
7 4.2
9 5.4
y
1.2
4
8
2.4
13 3.9
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Answer:
The question is unclear. Please provide the table.
use substitution to solve the system of equations. Write the solution as an ordered pair.
x + 2y = 14
y = 3x - 14
Answers
Answer:
Step-by-step explanation:
x + 2(3x - 14) = 14
x + 6x - 28 = 14
7x - 28 = 14
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x = 6
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Answer:
$18,000
Step-by-step explanation:
Trust me it's right
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Answers
Answer:
The standard deviation is the best measurement of spread for games and movies.
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Answers
Answer:
28.26 cm²
Step-by-step explanation:
Area of a circle = πr²
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Answers
Answer:
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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
10. *
10. If Talia's old bedroom measured 10
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Answers
Answer:
A
Step-by-step explanation:
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, 3) and (3, 4). Everything above the line is shaded. The second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). Everything to the right of the line is shaded.
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Answers
Answer:
A. y≥[tex]\frac{1}{3\\}[/tex]x+3, 3x-y>2
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.
The system of inequality is
[tex]x-3y\leq -9[/tex]
[tex]3x-y>2[/tex]
Points of the first line
[tex](0,3)[/tex]
[tex](3,4)[/tex]
The equation of the line is
[tex]y-3=\dfrac{4-3}{3-0}(x-0)\\\Rightarrow y-3=\dfrac{1}{3}x\\\Rightarrow y-\dfrac{1}{3}x=3\\\Rightarrow 3y-x=9\\\Rightarrow x-3y=-9[/tex]
Let us take a point above this line [tex](2,4)[/tex]
It is also a solid line.
[tex]2-3\times 4=-10<-9[/tex]
So, the inequality is [tex]x-3y\leq -9[/tex]
Points of the second line
[tex](0,-2)[/tex]
[tex](1,1)[/tex]
The equation of the second line is
[tex]y+2=\dfrac{1+2}{1-0}(x-0)\\\Rightarrow y+2=3x\\\Rightarrow 3x-y=2[/tex]
Let us take a point towards the right of the line [tex](2,2)[/tex]
[tex]3\times 2-2=4>2[/tex]
Since, the line is dashed the second inequality will be [tex]3x-y>2[/tex]
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https://brainly.com/question/13447558?referrer=searchResults
one divided by eight over nine
Answers
[tex]\frac{1/8}{9}[/tex] is the answer.
Brainiest if possible? thnx
what is the answer to this question
Answers
Answer:
the height is 4
Step-by-step explanation:
it is a right triangle and also a perfect 3-4-5 right triangle
[tex] {3}^{2} + {h}^{2} \: equals \: {5}^{2} [/tex]
[tex]9 + {h}^{2} \: eqauls \: 25[/tex]
subtract 9 from 25
[tex] {h}^{2} \: equals \: 16[/tex]
then you square root 16
[tex] \sqrt{16} [/tex]
and now you height is 4
3x + 160y<=1120 written in slope intercept form
Answers
PLEASE HELP ME!!
let g be the function given by g (x) = 3x^4 - 8x^3. At what value of x on the closed interval [ -2,2 ] does g have an absolute maximum
Answers
g’(x) = 12x^3 - 24x^2
Set equal to zero and solve:
0 = 12x^3 - 24x^2
0 = 12x^2 (x - 2)
x = 0 or x = 2
Plug back into original
g(0) = 3(0^4) - 8(0^3)
g(0) = 0 - 0
g(0) = 0
g(2) = 3(2^2) - 8(2^3)
g(2) = 3(4) - 8(8)
g(2) = 12 - 64
g(2) = -52
There is an absolute max at (0,0) or when x = 0
The value of x on the closed interval [ -2,2 ] that g has an absolute maximum is 0
Given the function [tex]g (x) = 3x^4 - 8x^3[/tex]
The function is at a maximum at g'(x) = 0
Differentiating the function given:
[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]
Substitute x = 0 and x = 2 into the function;
g(0) = 3(0)^3 - 8(0)^3
g(0) = 0
Since the range of the function is least at x = 0, hence the value of x on the closed interval [ -2,2 ] that g has an absolute maximum is 0
Learn more function here: https://brainly.com/question/10439235
9 sec x + 9 tan x = 9
Answers
Answer:
Lowest root is 0 degrees.
Step-by-step explanation:
divide through by 9:
sec x + tan x = 1
sec^2x = 1 + tan^2 x so
√(1 + tan^2x) + tanx = 1
√(1 + tan^2x) = 1 - tanx
Squaring both sides:
1 + tan^2 x = 1 - 2 tanx + tan^2 x
1 = 1 - 2 tan x
2tanx = 0
x = 0 degree.