What Is the Height of the Pole in This Trigonometry Problem?

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Discussion Overview

The discussion revolves around a trigonometry problem involving the calculation of the height of a pole based on the angle of elevation from a man standing a certain distance away. The scope includes mathematical reasoning and problem-solving approaches related to trigonometric functions.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes a setup using the tangent function to relate the height of the pole to the height of the man and the distance from the pole.
  • Another participant suggests an alternative formulation, defining the height of the pole in terms of the difference between the pole's height and the man's height, leading to a calculation involving tangent.
  • There are multiple formulations of the tangent function, with one participant questioning the relationship and suggesting a different equation involving the height difference.
  • Another participant reiterates the tangent function's definition and proposes using the cotangent function instead, which is acknowledged as correct by another participant.

Areas of Agreement / Disagreement

Participants express different approaches to the problem, with no consensus on a single method or solution. Multiple competing views remain regarding the setup and equations used.

Contextual Notes

Some participants' equations depend on specific interpretations of the problem setup, and there are unresolved mathematical steps in the various approaches presented.

mathdad
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A little review of trigonometry.

A man 1.5m tall is standing 4m away from a pole. If the angle of elevation of the top of the pole is 30 degree,
calculate the height of the pole.

My set up is here.

Let x = height of pole

1.5 + tan30 = x/4

4*tan(30) = x + 4(1.5)

Correct?
 
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I would let P (in m) be the height of the pole, and let x be the difference between the height of the pole and the height of the man, i.e.:

x = P - 1.5

or:

P = x + 1.5

Constructing a right triangle, we obtain:

tan(30°) = x/4 which implies x = 4 tan(30°)

And so we have:

P = 4 tan(30°) + 1.5

$$P=\frac{4}{\sqrt{3}}+\frac{3}{2}=\frac{8+3\sqrt{3}}{2\sqrt{3}}=\frac{9+8\sqrt{3}}{6}\approx3.809401076758503$$
 
How about tan(30) = 4/(x - 1.5)?
 
RTCNTC said:
How about tan(30) = 4/(x - 1.5)?

You would want:

tan(30°) = (x - 1.5)/4

The tangent function represents the ratio of opposite/adjacent in a right-triangle. :D
 
MarkFL said:
You would want:

tan(30°) = (x - 1.5)/4

The tangent function represents the ratio of opposite/adjacent in a right-triangle. :D

How about cot(30) = 4/(x - 1.5)?
 
RTCNTC said:
How about cot(30) = 4/(x - 1.5)?

Yes, that would be correct. :D
 
Cool. Now back to precalculus. Check out my absolute value questions.
 

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