Unraveling a Trigonometric Mystery

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SUMMARY

The discussion focuses on solving a trigonometric problem involving the tangent function. The equation derived is tan(20) = x/25, where x represents the height of an eagle above a person's eye level, and the base of the triangle is 25 feet. To find the total height of the eagle above the ground, an additional 5 feet must be added to the calculated height (x). This highlights the importance of understanding the context of trigonometric measurements in real-world applications.

PREREQUISITES
  • Understanding of basic trigonometric functions, specifically tangent.
  • Familiarity with right triangle properties and definitions.
  • Ability to manipulate algebraic equations.
  • Knowledge of how to apply trigonometric principles to real-world scenarios.
NEXT STEPS
  • Study the properties of right triangles in trigonometry.
  • Learn about the applications of the tangent function in various fields.
  • Explore how to calculate heights using trigonometric ratios in practical situations.
  • Investigate the relationship between angles and side lengths in trigonometric functions.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and professionals applying trigonometric principles in fields such as engineering and architecture.

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We know the answer, but don't know how it makes sense given trigonometric principles.

View attachment 9219

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.
 

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