Answer: Approximately 12719 feet
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Explanation:
See the diagram below.
We have the following points
- A = Plane's location.
- B = car #1's location.
- C = car #2's location
.
- D = point directly above point B (same horizontal level as point A).
- E = point directly above point C (same horizontal level as point A).
The goal is to find the length of segment BC, which is the distance between the two cars. For now, let's call it x.
Note how quadrilateral BCED is a rectangle. This means that the opposite sides BC and ED are the same length. Furthermore, note how segment ED is broken up into DA and AE, which I'll call m and n.
So we have these variable assignments
- x = length of segment BC
- m = length of segment DA
- n = length of segment AE
We'll find the values of m and n, so we can then find the value of x. We can see that x = m+n.
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Let's focus entirely on triangle ABD
Apply a tangent ratio to solve for m
tan(angle) = opposite/adjacent
tan(A) = BD/AD
tan(32) = 5150/m
m*tan(32) = 5150
m = 5150/tan(32)
m = 8241.7228245614
This value is approximate. Make sure your calculator is in degree mode.
We'll come back to this later.
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Now focus entirely on triangle CEA. We'll apply the tangent rule again.
tan(angle) = opposite/adjacent
tan(A) = EC/AE
tan(49) = 5150/n
n*tan(49) = 5150
n = 5150/tan(49)
n = 4476.82669975357
This value is approximate.
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Now we can find x.
x = m+n
x = 8241.7228245614 + 4476.82669975357
x = 12718.549524315
x = 12719
The distance between the two cars is roughly 12719 feet
I'm rounding to the nearest whole number because the other values were given to be whole numbers.
Side note: 12719 ft = 2.41 miles approximately (divide by 5280 to convert from feet to miles).
