SOLUTION: A plane is observed approaching your home at a speed of 600 miles per hour. If the angle of elevation of the plane is 16 degrees at one time and 48 degrees one minute later, find

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Question 1131113: A plane is observed approaching your home at a speed of 600 miles per hour. If the angle of elevation of the plane is 16 degrees at one time and 48 degrees one minute later, find the approximate altitude of the plane.
Answer approximately 3.865 miles. How would I set this problem up?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A plane is observed approaching your home at a speed of 600 miles per hour.
If the angle of elevation of the plane is 16 degrees at one time and 48 degrees one minute later, find the approximate altitude of the plane.
:
Find how far the plane travels in 1 min: 600/60 = 10 mi
:
let h = the height of the plane above the ground
let x = the distance from the 1st angle position to the 2nd angle position
:
two right triangles are formed, in both triangles the side opposite = h
In the 1st triangle the side adjacent = (x+10)
In the 2nd triangle the side adjacent = x
:
tan(16) = h%2F%28%28x%2B10%29%29
solve for h
h = tan(16)(x+10)
and
tan(48) = h%2Fx
h = tan(48)*x
:
h = h, so we can write the equation to solve for x
tan(48)*x = tan(16)(x+10)
1.1106x = .2867x + 2.867
1.1106x - .2867x = 2.867
.8239x = 2.867
x = 2.867%2F.8239
x = 3.48 mi
:
Find h with the 48 degree triangle
h = tan(48)*3.48
h = 3.8647 mi is the altitude
:
Check this by finding h using the 16 degree equation
h = tan(16)(3.48+10))
h = tan(16)*13.48
h = 3.8653 mi, very close



Answer approximately 3.865 miles. How would I set this problem up?