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
a taxicab company charges $2.10 and $0.80 a mile. Sheila took a cab and paid a fare of $11.70.Which equation represents this situation with the correct number of miles?
Answers
Answer:
D 2.10+0.80m=11.70, 12 miles
Step-by-step explanation:
11.70-2.10=9.6
9.6/0.80=12
so there is 12 miles and only d has 12 miles
hope this helps have a blessed day
A line passes through the point (-8, – 4) and has a slope of 5/4 write an equation in point slope form
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One month lashonda rented 7 movies and 9 video games for a total of $73 the next month she rented 5 movies and 3 video games for a total of $29 find the rental cost for each movie and each video game
Answers
Answer:
Solve a system of equations with two unknowns x and y
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Step-by-step explanation:
Millie has a box of crayons. 30 of the crayons are red, 14 are green, and 16 are
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07
0 10
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Answers
Answer: i’m really not sure about this one but i think eight
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3. The point P(3,5) is rotated 90° clockwise
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P'?
A. P'(-3,-5)
B. P’(5,-3)
C. P'(-5,3)
D. P'(5, 3)
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Answers
Answer:
New coordinates of P' are: P'(5, -3)
Hence, option B i.e. P'(5,-3) is correct.
Step-by-step explanation:
When a point A(x, y) is rotated 90° clockwise around the origin, we flip x and y and reverse the sign of x.
Thus,
The rule to rotate a point A(x, y) after a rotation 90° counterclockwise around the origin is:
A(x, y) → A'(y, -x)
In our case, the point P(3, 5) is rotated 90° clockwise about the origin. Thus, the coordinates of P' will be:
A(x, y) → A'(y, -x)
P(3, 5) → P'(5, -3)
Therefore, coordinates of P' are: P'(5, -3)
Hence, option B i.e. P'(5,-3) is correct.
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Answers
It takes 4 pounds of apples to make 6 cups of applesauce.
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Group of answer choices
5:7
10:15
6:9
1:2
14:21
8:10
Answers
Answer:
Step-by-step explanation:
4lbs of apples to 6 cups of apple sauce
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Answers
Answer:
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Step-by-step explanation:
Answer:
Should be step 2!
Step-by-step explanation:
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Answer:
Inequality Form:
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Interval Form:
(-23, ∞)
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Answer:
2 3/4+(2 3/4 / 2)=t
Step-by-step explanation:
IM sure this is right
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Answers
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Answer:
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Step-by-step explanation:
Answer:
the third option, C (6,0)
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Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
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height- 2
Answers
Answer: 87.9
Step-by-step explanation:
Since the formula is 2 x pi x radius x height, we plug the equation in.
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Needdddddd helpppppppp ASAP
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Answer:
4th option, always increasing
Step-by-step explanation:
It’s always increasing because the graph is concave up
If you get it right/wrong, do let me know
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Answer:
1. false
2. true
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Step-by-step explanation:
1. 128 is not equal to 125
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48-7)x(56+19 need help with dat
Answers
Answer:
3075 should be the answer.
Step-by-step explanation:
48-7)x(56+19
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Answers
The corresponding angles are
2 and 6
3 and 7
5 and 3
and, 4 and 8
What are corresponding angles?
Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are called corresponding angles.
Or, when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
According to the given question.
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From the given diagram,
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Therefore, we can say that angles
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3 and 7
5 and 3
and, 4 and 8
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Which inequality is represented by this graph?
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Answers
Answer:
B. X > 0
Step-by-step explanation:
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Coupon A-14$ rebate on 77$ jacket
Coupon B- 15% off on a 77$ jacket
Answers
I WILL GIVE 10 POINTS IF YOU ANSWER CORRECTLY AND I WILL GIVE THE BRAINLIEST.
Answers
Answer:
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Step-by-step explanation:
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1. What is the volume of the cylinder shown above, rounded to the nearest hundredths?
2. What is the volume of the cylinder shown above if the radius is doubled, rounded to the nearest hundredths?
3. What is the volume of the cylinder shown above if the height is cut in half, rounded to the nearest hundredths?
Answers
Answer:
1) 169.7
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Which fraction is equal to 0.5 7?
A. 19/30
B. 19/33
C. 26/45
D. 52/99
Answers
The correct answer for fraction equal to 0.57 is [tex]\dfrac{19}{33}[/tex] and [tex]\dfrac{26}{45}[/tex]. The correct 0ptions are C and B.
What is fraction?
A fraction is a numerical value that has both numerator and denominator.
Given Number:
A)
[tex]\dfrac{19}{30} = 0.63[/tex]
[tex]0.63[/tex] ≠ [tex]0.57[/tex]
B)
[tex]\dfrac{19}{33} = 0.5757[/tex]
[tex]0.57 = 0.57[/tex]
C)
[tex]\dfrac{26}{45} = 0.5777[/tex]
[tex]0.57 = 0.57[/tex]
D)
[tex]\dfrac{52}{99} = 0.52[/tex]
[tex]0.57[/tex] ≠ [tex]0.52[/tex]
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Answers
Answer:
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Step-by-step explanation:
but if this gives you youre points , there you go
Leyan bought 234 pounds of apples for $1.32 per pound, 112 pounds of peaches for $1.20 per pound, and some tomatoes, all from a grocery store. The total cost of his purchase was $9.63. How much money did Leyan spend on tomatoes?
Answers
Answer: See explanation
Step-by-step explanation:
I think your question isn't well written and that 234 was meant to be 2.34 and 112 was meant to be 1.12
Let the amount spent on tomatoes be x.
The information given in the question can then be used to form an equation as thus:
Apples + Peaches + Tomatoes = $9.63
(2.34 × $1.32) + (1.12 × $1.20) + x = $9.63
$3.0888 + $1.344 + x = $9.63
x = $9.63 - ($3.0888 + $1.344)
x = $9.63 - $4.4328
x = $5.1972
The amount spent on tomatoes will be $5.1972
Answer:
The answer is 4.2 I did this question already
Step-by-step explanation: You multiply 2 3/4 and 1.32 and then add that to the product of the 1 1/2 peaches for 1.20 per pound, then subtract the answer from 9.63 to get the solution for x.
Plzz help 15 points
Which of the following graphs show
f(x) =
x + 1, when x < 1
4, when ≥ 1
Answers
Answer:
I think its C if I'm wrong, sorrryyy
Write a linear equation to represent the line shown on the graph.
Answers
Answer:
x=1
Step-by-step explanation:
x=1
Answer:
Hello did have actual quiz it looks like i have the same quiz could yopu send that quiz to me thanks
Step-by-step explanation:
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What is the name of the parent function for f(x)=2 x-1
Answers
Answer:
Linear Function
Step-by-step explanation:
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Answer:
-2
Step-by-step explanation:
2, 1, 0, -1
If the pattern continues it will lead to the next number being - 2
Answer:
The answer is
[tex]y = - \frac{1}{4} x[/tex]
Step-by-step explanation:
[tex]y = - \frac{1}{4} \times - 8 = 2 \\ y = - \frac{1}{4} \times - 4 = 1 \\ y = - \frac{1}{4} \times 0 = 0 \\ y = - \frac{1}{4} \times 4 = - 1[/tex]
