What is the formula for finding angle theta without accounting for height?

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Discussion Overview

The discussion revolves around finding the angle theta (t) using trigonometric functions, specifically the tangent function, without initially accounting for the height of a person in relation to a tower. Participants explore different formulations and approaches to the problem.

Discussion Character

  • Mathematical reasoning, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant proposes using the formula tan(t) = 324/550 to find theta, applying the arctan function to derive the angle.
  • Another participant suggests an alternative formulation for tan(theta) that includes a height adjustment: tan(theta) = (324 - 1.6)/550.
  • Several participants express confusion about the initial approach and highlight the oversight of not accounting for the height of the person in the calculations.
  • A later reply acknowledges the omission of height and provides a corrected formula that incorporates the height of the tower and the person.

Areas of Agreement / Disagreement

Participants generally agree that the height of the person must be considered in the calculations, but there is no consensus on the initial approach or the specific formulas used.

Contextual Notes

The discussion reflects varying assumptions about the setup, particularly regarding the heights involved and their impact on the calculations. The mathematical steps leading to the proposed formulas are not fully resolved.

Who May Find This Useful

Individuals interested in trigonometry, particularly in applications involving angles and heights, may find this discussion relevant.

xyz_1965
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AngleofElevationEx1a.png.cf.png


Here is my set up.

Let t = theta for short

tan(t) = 324/550

arctan(tan t) = arctan(324/550)

t = arctan(324/550)

Correct thus far?

Note: What does "not to scale" mean in other words?
 
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$\tan{\theta} = \dfrac{324-1.6}{550}$
 
skeeter said:
$\tan{\theta} = \dfrac{324-1.6}{550}$

What is wrong with my approach?
 
xyz_1965 said:
What is wrong with my approach?

You aren't accounting for the height of the person.
 
MarkFL said:
You aren't accounting for the height of the person.

Ok. I totally forgot about the height of the person.

tan (theta) = (height of tower - height of person)/(distance between person and the base of the tower). This will help me when I face a similar problem again.
 

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