SOLUTION: From an observation tower two markers are viewed on the ground . The markers and the base of the tower are on a line and the observer's eye is 63.5 feet above the ground . The angl

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Question 878690: From an observation tower two markers are viewed on the ground . The markers and the base of the tower are on a line and the observer's eye is 63.5 feet above the ground . The angle of depression to the markers are 53.2 degrees and 27.8 degrees. How far is it from one marker to the other?
Can you please help me out ? Thanks so much in advance:)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Draw this figure yourself so that you can see all the details:
A tower represented as a segment, B at the base, the segment 63.5 units; a horizontal line extending from B, and on the line are points N and F being the two markers. This all forms two right triangles which share the right angle at point B. Because of parallel lines and angles formed (from the horizontal line referenced with elevation), the angle measure at N toward the tower is 53.2 degree and the angle at F toward the tower is 27.8 degree.

I chose N for the "near" marker, and F for the "far" marker; N is between B and F.

You want to know NF.
NF=BF-BN. You can use the tangent function values for the angles at N and F.
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highlight_green%28tan%2827.8%29=63.5%2FBF%29 and highlight_green%28tan%2853.2%29=63.5%2FBN%29
and the finishing steps are undone, for you to do.