kaitlynhuizaroy4ok4
kaitlynhuizaroy4ok4 kaitlynhuizaroy4ok4
  • 18-07-2018
  • Mathematics
contestada

A parallelogram with sides of 6 and 10 has an area of 30 times the square root of 2. Find the measure of the small angle of the parallelogram.

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jdoe0001 jdoe0001
  • 18-07-2018

check the picture below.


[tex] \bf 30\sqrt{2}=10h\implies \cfrac{30\sqrt{2}}{10}=h\implies \boxed{3\sqrt{2}=h}\\\\
-------------------------------\\\\
sin(\theta )=\cfrac{\stackrel{opposite}{3\sqrt{2}}}{\stackrel{hypotenuse}{6}}\implies sin(\theta )=\cfrac{\sqrt{2}}{2}
\\\\\\
\measuredangle \theta sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right)\implies \measuredangle \theta =\cfrac{\pi }{4}\textit{or just }45^o [/tex]

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