MHB How Do You Find the Measure of ∠BAC in Degrees?

[CGuthrie91]

View attachment 2416

Find the measure of angle $\angle BAC$.

 

[Prove It]

Re: Find the measure <BAC

Surely $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$. Can you see why?

 

[CGuthrie91]

Re: Find the measure <BAC

Surely $\displaystyle \begin{align*} \angle BAC = 34^{\circ} - 8^{\circ} \end{align*}$. Can you see why?

not really

 

[CGuthrie91]

What about the measure of <ABC?

 

[MarkFL]

What about the measure of <ABC?

View attachment 2417

What must the sum of the three angles I have labeled be?

 

[Prove It]

Re: Find the measure <BAC

not really

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]

https://www.physicsforums.com/attachments/2417

What must the sum of the three angles I have labeled be?

180?

 

[MarkFL]

180?

Yes, in degrees. So, can you set up an equation, and then solve for the unknown $x$, representing $\angle ABC$?