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

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The discussion focuses on calculating angle theta (t) using the tangent function, specifically with the equation tan(t) = 324/550. The user initially neglects to account for the height of the person in their calculations, which is crucial for accuracy. The correct approach involves using the formula tan(theta) = (height of tower - height of person) / (distance from the person to the tower). Acknowledging the height of the person is essential for solving similar problems in the future. This highlights the importance of considering all relevant variables in trigonometric calculations.
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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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