looking at a building on top of which an antenna is mounted.

[77Fabian]

Hi, I have the same problem as is given here.

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A person is looking at a building, on top of which an antenna is mounted. The horizontal distance between the person's eyes and the building is 85.0 m. When the person is looking at the base of the antenna, his line of sight ("part a") makes an angle of 35.0° with the horizontal. When the person is looking at the top of the antenna, his line of sight ("part b") makes an angle of 38.0° with the horizontal. How tall is the antenna?

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The helper's reply was:

Did you make a diagram?. This is an exercise in the law of tangents.

Let x=heigth of antennae and y=height of building.

We can see the height of the antennae is the difference in the tangents.

[FONT=MathJax_Main]85[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]38[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]85[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Math]n[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]35[/FONT][FONT=MathJax_Main])[/FONT]

Do you follow how I got that?

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Now when I come to doing the tangents individually, I receive 40.3m for part A, and 26.4 M for part B.

Can you please explain why we are taking the difference? I would naturally assume to add my results. Especially with theta being known.

Why is Ho greater in A where theta is 35 compared to less with theta having a higher degree - 38?

Thanks!

 

[stapel]

Now when I come to doing the tangents individually, I receive 40.3m for part A, and 26.4 M for part B.

Can you please explain why we are taking the difference?

For what does "x" stand? For what does "y" stand? How do the two tangent ratios relate to x and y? What value have you been asked to find?

If you were to add the values from the two tangent ratios, wouldn't you be adding the height of the building and antenna to the height of the antenna? Is this helpful?