SOLUTION: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure
Here is the ima
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Question 932230: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure
Here is the image:
http://i.imgur.com/OImRqbV.png
Please explain
Thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Problem:
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Solution:
(a)
Let P be the point where the plane is currently located. The length of AP is the same as the value of b (as shown below in the diagram)
Notice how the angle of depression corresponds to the congruent angle of elevation. Also I got the 100 degrees from the fact that 180-28-52 = 100
Use the law of sines to solve for b
Use a calculator here to get an approximate result
Round to 2 decimal places
Drop the trailing zeros
So b is approximately 4 miles. This is the distance from point A to the plane.
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(b)
Draw in the altitude or height (shown in blue)
Label it h for now.
Using trig, we know
Plug in
Use a calculator here.
Round to 2 decimal places
The value of h is approximately 1.88 miles.
So the elevation of the plane is approximately 1.88 miles.
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