Trigonometry 3d pyramid question

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Homework Help Overview

The discussion revolves around a trigonometry problem involving a 3D pyramid, specifically focusing on calculating an angle (theta) using the cosine law and the Pythagorean theorem. Participants are trying to reconcile their calculations with an answer key that suggests a different angle measurement.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to calculate the angle theta using various lengths and angles provided in the problem. There are questions about which lengths correspond to specific points in the diagram, particularly regarding the length of 15 cm. Some participants express confusion over the notation and the implications of the angles assumed in the calculations.

Discussion Status

There is ongoing exploration of the problem, with participants providing their calculations and questioning the assumptions made regarding the triangle's configuration. Some have noted discrepancies between their results and the answer key, leading to further inquiry into the problem's setup.

Contextual Notes

Participants highlight the ambiguity in the diagram, particularly concerning the lengths and angles involved. There is a suggestion that the diagram may not be to scale, which could affect the interpretation of the problem. Additionally, the lack of clarity about which lengths correspond to which points is noted as a potential source of confusion.

needingtoknow
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Homework Statement



http://imgur.com/x8D2wqO

I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?
 
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It isn't quite clear what length is 15cm. Is it AC or AD? To get 93 degrees, it would probably have to be AC. Either way, there does not seem to be enough information. Please post your working.
 
15 cm is AD
 
c^2 = a^2 + b^2 - 2abcosC
c = 23.7471

h^2 = a^2 + b^2
h = 23.4307

h^2 = a^2 + b^2
h = 20.5183

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65
 
needingtoknow said:
c^2 = a^2 + b^2 - 2abcosC
c = 23.7471

h^2 = a^2 + b^2
h = 23.4307

h^2 = a^2 + b^2
h = 20.5183

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65
I can't be expected to follow that if you keep changing what the letters refer to and don't specify each time.
 
Using AD = 15cm, BD = 18cm, CD = 14cm and angle BDC = 95 degrees, I too get 65 degrees as angle BAC.
 
c^2 = a^2 + b^2 - 2abcosC
c = 23.7471 Finding length of BC

h^2 = a^2 + b^2
h = 23.4307 Finding length of AB

h^2 = a^2 + b^2
h = 20.5183 Finding length of AC

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65 Finding angle theta of triangle ABC
 
After making some guesses about the other assignments in those equations, I'm led to suppose you are taking angles ADB, ADC to be right angles. I don't see that stated anywhere.
As I said, to get an angle of over 90 degrees as the answer, you will need the 15cm to refer to AC, not AD. OTOH, I then get 91.9 degrees, so it still doesn't seem quite right.
 
All right so it must be a textbook answer key problem. Thank you very much for your help
 

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