Trigonometry: Wanting someone to check my answer for Statics

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Discussion Overview

The discussion revolves around a homework problem involving trigonometry and statics, specifically calculating the angle at which a building is leaning after an earthquake. Participants are reviewing the solution approach and calculations provided by the original poster.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • The original poster presents a problem involving a building's height and distance from a surveyor, seeking confirmation on their calculations for the angle of lean.
  • Some participants affirm the correctness of the original poster's calculations, indicating that the use of the sine law is appropriate for determining angle C.
  • One participant notes a potential issue if angle beta were smaller or if the building height were less, suggesting that angle C might exceed 90 degrees in those scenarios.
  • The original poster expresses uncertainty regarding the steepness of the angle as suggested by an accompanying image, despite receiving positive feedback on their calculations.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the calculations presented, but there is an acknowledgment of potential issues under different conditions, indicating that the discussion remains open to interpretation.

Contextual Notes

The discussion does not resolve the implications of the angle exceeding 90 degrees or the impact of the building's height on the calculations.

blixel
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Homework Statement


A building is 400 ft tall and has suffered damage from a recent earthquake. If a surveyor is stationed 150 ft away, sets a zero angle on the bottom corner of the building, and turns the angle shown to the top of the building; what is the angle at which the building is leaning with respect to vertical?

media2F5532F55321e7f-7f4c-4caa-802b-a8355fd584002Fimage_zpsxhvof20n.jpg


Homework Equations


I feel like I know what to do, but would like confirmation from the forum please.

The Attempt at a Solution


sin(70)/400 = sinC/150
sinC=[150*sin(70)]/400
C=arcsin([150*sin(70)]/400)~=20.6332
180-70-20.6332=89.3668

Therefore, Beta = 89.3668
 

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Your work looks fine to me :smile:
 
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Seems correct to me. You use sine law to determine sinC and therefore C (provided that ##C<90##), and then knowing C and the angle of 70 degrees can determine the other angle of the triangle.

Just to add something if angle beta was smaller or the building height was not so big, angle C might have been >90 degrees.
 
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gneill said:
Your work looks fine to me :smile:

Thanks for checking it over. The work felt right, but the image suggests a steeper angle, so I wasn't confident.
 

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