Question 1013229
i'm not sure where the 50 feet comes from.
let me see what i can do without that.


the plane is flying at 10,500 feet.


the angle of depression from the plane to the base of the tree is 13 degrees, if i understand that correctly.



the angle of depression is the angle that is formed by drawing a line that is 13 degrees from the horizontal line formed by the plane.


see the following reference for a discussion of angle of elevation and angle of depression.


<a href = "http://www.purplemath.com/modules/incldecl.htm" target = "_blank">http://www.purplemath.com/modules/incldecl.htm</a>


you have two horizontal lines at AD and CB.
you have two vertical lines at AC and DB.


the length of line AC is equal to the length of DB.
the length of AD is equal to the length of CB.


the angles at A, B, C, D, are all 90 degrees.


ADBC is therefore a rectangle.


the length of AD and CB is represented by x in the diagram.


since line AD and CB are parallel, and since line AB is a transversal of those two parallel lines, then angle DAB is congruent to angle ABC, so they're both equal to 13 degrees.


tan(angle ABC) = tan(13) = 10500 / x.


solve for x to get x = 10500 / tan(13) = 45480.49668.


x is the horizontal distance from the plane to the point D directly above the foot of the tree at point B.


that's your solution.


x = 45480.49668 feet.


round as you see fit.


here's the diagram of the triangles and rectangle formed.


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