MHB Unraveling a Trigonometric Mystery

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The discussion centers on understanding a trigonometric problem involving a right triangle and the tangent function. The tangent of the 20-degree angle is defined as the ratio of the opposite side to the adjacent side, leading to the equation tan(20) = x/25, where x represents the height of an eagle above eye level. To find the total height of the eagle above the ground, the 5 feet from the person's eye level must be added to the calculated height. This highlights the importance of considering all relevant measurements in trigonometric problems. The conversation emphasizes the need to clarify how the calculated height relates to the overall scenario.
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We know the answer, but don't know how it makes sense given trigonometric principles.

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Borrowed from HiSet free practice test
 

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Hint: Tan = height/base
 
As monoxdifly said, "tangent" is "opposite side over near side". Looking at the right triangle in tne picture, the "opposite side" to the 20 degree angle has length "x" and the "near side" has length 25 feet. tan(20)= x/25 so x= 25 tan(20). But x is the height of the eagle above the person's eye level, not the height of the eagle above the ground. We have to add the 5 feet from the ground 5o the person's eye level.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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