Find angle B in the trigonometry problem

Thread starter chwala
Start date Aug 11, 2021
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Angle Trigonometry

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SUMMARY

The discussion centers on finding angle B in a trigonometry problem involving triangle properties and the Law of Sines. Participants utilized various methods, including trigonometric identities and geometric constructions, to derive that angle B equals 30 degrees. Key calculations involved using the sine rule and tangent ratios, specifically demonstrating that tan B equals 1/sqrt(3). The final consensus confirms that angle B is indeed 30 degrees through multiple proofs and approaches.

PREREQUISITES

Understanding of basic trigonometric functions (sine, cosine, tangent)
Familiarity with the Law of Sines and Law of Cosines
Ability to perform algebraic manipulations with trigonometric identities
Knowledge of geometric constructions and properties of triangles

NEXT STEPS

Study the Law of Sines and its applications in triangle problems
Learn how to derive and manipulate trigonometric identities
Explore geometric constructions related to triangle similarity
Practice solving trigonometric equations without a calculator

USEFUL FOR

Students, educators, and anyone interested in enhancing their understanding of trigonometry, particularly in solving angle-related problems in triangles.

Feb 10, 2023

neilparker62

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Charles Link said:

Very clever @neilparker62 :)

To show the triangles are similar, we need to show ##de/da=da/db ##. (These are corresponding sides around the same angle).
Now ## da/db=da/ac=\sin(40)/\sin(80) ##.
Meanwhile ## de/da=\sin(30)/\sin(50) ##.
We need to show ## \sin(40)/\sin(80)=\sin(30)/\sin(50)##.

With ## \sin(80)=2 \sin(40) \cos(40) ##, and ## \sin(30)=1/2 ##, and ## \cos(40)=\sin(50) ##, we have proven the triangles to be similar, and thereby angle ##B=30 ## degrees.

Yes I remembered now - my workings were with sin(100) rather than sin(80) but same thing obviously.