- #1
Albert1
- 1,221
- 0
How Do You Calculate the BC Angle in a Triangle?
- Context: MHB
- Thread starter Albert1
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Discussion Overview
The discussion revolves around calculating the angle BC in a triangle, specifically using trigonometric and geometric methods. Participants explore different approaches to arrive at the solution.
Discussion Character
- Technical explanation, Homework-related
Main Points Raised
- One participant uses trigonometric identities and Pythagorean theorem to derive lengths and angles in the triangle, concluding with the length of side BC.
- Another participant acknowledges the correctness of the first post and expresses a desire for a solution using only geometric methods, indicating a preference for an alternative approach.
Areas of Agreement / Disagreement
There is agreement on the correctness of the initial calculations, but a disagreement remains regarding the method of solution, as one participant seeks a purely geometric approach.
Contextual Notes
The discussion does not resolve the method preference, and the geometric approach remains unaddressed.
Who May Find This Useful
Readers interested in triangle geometry, trigonometry, and problem-solving methods in mathematics may find this discussion relevant.
- #2
Opalg
Gold Member
MHB
- 2,778
- 13
[sp]
By Pythagoras, $\overline{DE} = 6$. With angles $\alpha,\;\beta$ as marked in the diagram, $\tan\alpha = \frac34$. Therefore $$\tan\beta = \tan(45^\circ - \alpha) = \frac{1-\frac34}{1 + \frac34} = \frac17.$$ So $\overline{BD} = \frac87$, and (Pythagoras) $\overline{AB} = \dfrac{40\sqrt2}7.$ It follows that $\overline{AC} = 40\sqrt2$, and (Pythagoras again) $\overline{BC} = \dfrac{400}7.$[/sp]
By Pythagoras, $\overline{DE} = 6$. With angles $\alpha,\;\beta$ as marked in the diagram, $\tan\alpha = \frac34$. Therefore $$\tan\beta = \tan(45^\circ - \alpha) = \frac{1-\frac34}{1 + \frac34} = \frac17.$$ So $\overline{BD} = \frac87$, and (Pythagoras) $\overline{AB} = \dfrac{40\sqrt2}7.$ It follows that $\overline{AC} = 40\sqrt2$, and (Pythagoras again) $\overline{BC} = \dfrac{400}7.$[/sp]
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- #3
Albert1
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thanks for your participation, your answer is correct !
this time using geometry only ,hope someone can do it
this time using geometry only ,hope someone can do it
- #4
Albert1
- 1,221
- 0
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