$\bf sin(2\theta)=2sin(\theta)cos(\theta)\\\\
-------------------------------\\\\
sin(2x)-\sqrt{3}cos(x)=0\implies 2sin(x)cos(x)-cos(x)\sqrt{3}=0
\\\\\\
\stackrel{\stackrel{common}{factor}}{cos(x)}[2sin(x)-\sqrt{3}]=0\\\\
-------------------------------\\\\$

$\bf cos(x)=0\implies \measuredangle x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\\\\
-------------------------------\\\\
2sin(x)-\sqrt{3}=0\implies 2sin(x)=\sqrt{3}\implies sin(x)=\cfrac{\sqrt{3}}{2}
\\\\\\
\measuredangle x=
\begin{cases}
\frac{\pi }{3}\\\\ \frac{2\pi }{3}
\end{cases}$

7 0

2 years ago

I was doing my homework and got confused on this question.

spayn [35]

We will determine the length of the segment DF as follows:

*We have that the triangles are similar, and therefore the following is true:

$\frac{2}{1.34}=\frac{4}{DF}$

Now, we solve for DF:

$\Rightarrow DF=\frac{1.34\cdot4}{2}\Rightarrow DF=2.68$

From this, we have that the length of the segment DF equals 2.68 units.

4 0

1 year ago