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CGuthrie91
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How Do You Find the Measure of ∠BAC in Degrees?
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SUMMARY
The measure of angle $\angle BAC$ is calculated as $\angle BAC = 34^{\circ} - 8^{\circ}$, resulting in $\angle BAC = 26^{\circ}$. This calculation is based on the angle of elevation at point A, which is $34^{\circ}$, and the angle formed by the slope of the ground, which is $8^{\circ}$. The sum of the angles in triangle ABC must equal $180^{\circ}$, allowing for further calculations of other angles such as $\angle ABC$.
PREREQUISITES- Understanding of basic trigonometry concepts
- Familiarity with angle measures in degrees
- Knowledge of the properties of triangles
- Ability to set up and solve equations
- Study the properties of triangles and the sum of angles in a triangle
- Learn how to calculate angles of elevation and depression
- Explore trigonometric functions and their applications in solving for unknown angles
- Practice solving equations involving angles in geometric figures
Students studying geometry, educators teaching trigonometry, and anyone interested in understanding angle calculations in triangles.
- #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?
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CGuthrie91
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Re: Find the measure <BAC
not really
Prove It said:
not really
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CGuthrie91
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What about the measure of <ABC?
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MarkFL
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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:
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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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