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3 years ago

A figure is shown Below Find M

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

7 0

Answer:

58 degrees

Step-by-step explanation:

We know that angles on a straight add up to 180 degrees. Therefore:

To find the angle at the top of the triangle do 180-112 = 68

To find the angle at the right side of the triangle do 180 - 126 = 54

We know that angles in a triangle add up to 180 degrees. Therefore:

To find m do 180 - (54 + 68) = 58

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Can someone help me with b and c?

earnstyle [38]

$\bf \textit{Half-Angle Identities}
\\ \quad \\
sin\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{1-cos({{ \theta}})}{2}}\qquad 
\boxed{cos\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{1+cos({{ \theta}})}{2}}}$

$\bf tan\left(\cfrac{{{ \theta}}}{2}\right)=
\begin{cases}
\pm \sqrt{\cfrac{1-cos({{ \theta}})}{1+cos({{ \theta}})}}
\\ \quad \\

\cfrac{sin({{ \theta}})}{1+cos({{ \theta}})}
\\ \quad \\

\cfrac{1-cos({{ \theta}})}{sin({{ \theta}})}
\end{cases}\\\\
-----------------------------\\\\$

$\bf so\qquad 
\begin{cases}
2\cdot \cfrac{1}{8}\implies \cfrac{1}{4}\qquad thus\implies \cfrac{\frac{1}{4}}{2}\implies \cfrac{1}{8}\\\\
2\cdot \cfrac{1}{16}\implies \cfrac{1}{8}\qquad thus\implies \cfrac{\frac{1}{8}}{2}\implies \cfrac{1}{16}
\end{cases}\\\\
-----------------------------\\\\$

$\bf cos\left( \cfrac{\pi }{8} \right)\iff cos\left( \cfrac{\frac{\pi }{4}}{2} \right)
\\\\\\
cos\left( \cfrac{\frac{\pi }{4}}{2} \right)=\pm \sqrt{\cfrac{1+cos\left( \frac{\pi }{4} \right)}{2}}\implies \pm \sqrt{\cfrac{1+\frac{\sqrt{2}}{2}}{2}}\\\\
-----------------------------\\\\
cos\left( \cfrac{\pi }{16} \right)\iff cos\left( \cfrac{\frac{\pi }{8}}{2} \right)
\\\\\\
cos\left( \cfrac{\frac{\pi }{8}}{2} \right)=\pm \sqrt{\cfrac{1+cos\left( \frac{\pi }{8} \right)}{2}}$

and what is $\bf cos\left( \cfrac{\pi }{8} \right) \ ?$ well, you've just got it from the previous exercise :)

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