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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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.
 

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