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

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SUMMARY

The discussion focuses on calculating the angle theta (t) using the tangent function, specifically in the context of a right triangle formed by a tower and a person. The correct formula for theta is established as tan(t) = (height of tower - height of person) / distance from the person to the base of the tower. The initial approach incorrectly omitted the height of the person, leading to an inaccurate calculation. The final formula emphasizes the importance of including all relevant heights in trigonometric calculations.

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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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