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CGuthrie91
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How Do You Find the Measure of ∠BAC in Degrees?
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Discussion Overview
The discussion revolves around finding the measure of angle $\angle BAC$ in a geometric context. Participants explore relationships between angles, specifically involving angle elevation and the sum of angles in a triangle.
Discussion Character
- Mathematical reasoning, Homework-related, Conceptual clarification
Main Points Raised
- Some participants propose that $\angle BAC$ can be calculated as $34^{\circ} - 8^{\circ}$, suggesting a relationship between the angle of elevation and another angle.
- One participant questions the reasoning behind the calculation of $\angle BAC$ and expresses uncertainty about the initial claim.
- Another participant introduces the measure of angle $\angle ABC$ and raises a question about the sum of the angles in the triangle.
- There is a suggestion that the sum of the three angles labeled must equal 180 degrees, prompting further inquiry into setting up an equation to solve for an unknown angle.
Areas of Agreement / Disagreement
Participants express differing levels of understanding regarding the calculation of $\angle BAC$, and there is no consensus on the reasoning behind the proposed measures. The discussion remains unresolved with multiple viewpoints on the relationships between the angles.
Contextual Notes
Participants reference the angle of elevation and the relationship between angles without fully resolving the mathematical steps or assumptions involved in their reasoning.
- #2
Prove It
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Re: Find the measure <BAC
Surely $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$. Can you see why?
Surely $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$. Can you see why?
- #3
CGuthrie91
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Re: Find the measure <BAC
not really
Prove It said:
not really
- #4
CGuthrie91
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What about the measure of <ABC?
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MarkFL
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Prove It
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Re: Find the measure <BAC
The angle of elevation is $\displaystyle \begin{align*} 34^{\circ} \end{align*}$. This is the angle at point A that the segment AB makes with the horizontal.
The angle at A that is made from the slope of the ground with the horizontal is $\displaystyle \begin{align*} 8^{\circ} \end{align*}$. This combined with $\displaystyle \begin{align*} \angle BAC \end{align*}$ gives the angle of elevation.
So $\displaystyle \begin{align*} \angle BAC + 8^{\circ} = 34^{\circ} \end{align*}$, or equivalently, $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$.
CGuthrie91 said:
The angle of elevation is $\displaystyle \begin{align*} 34^{\circ} \end{align*}$. This is the angle at point A that the segment AB makes with the horizontal.
The angle at A that is made from the slope of the ground with the horizontal is $\displaystyle \begin{align*} 8^{\circ} \end{align*}$. This combined with $\displaystyle \begin{align*} \angle BAC \end{align*}$ gives the angle of elevation.
So $\displaystyle \begin{align*} \angle BAC + 8^{\circ} = 34^{\circ} \end{align*}$, or equivalently, $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$.
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CGuthrie91
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180?MarkFL said:
- #8
MarkFL
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CGuthrie91 said:
Yes, in degrees. So, can you set up an equation, and then solve for the unknown $x$, representing $\angle ABC$?
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