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In triangle DEF, DF=22 and angle F=45. Find the length of a leg. Leave your answer in simplest radical form.

Options:
1.) sqrt2
2.) sqrt11
3.) 11sqrt2
4.) sqrt22
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In triangle DEF DF22 and angle F45 Find the length of a leg Leave your answer in simplest radical formOptions1 sqrt22 sqrt113 11sqrt24 sqrt22 class=


Answer :

sqrt{2} = [tex]\sqrt{2}[/tex]

Given that

DF is the hypotenuse, we have:

DF = x sqrt{2}

x is the length of each leg.

Since DF = 22, we can setup the equation:

22 = x sqrt{2}

To simplify, we rationalize the denominator:

x = 22/[tex]\sqrt{2}[/tex] * sqrt{2} / sqrt{2} = 22sqrt{2}/2 = 11sqrt{2}

Thus, the length of each leg is:

11[tex]\sqrt{2}[/tex]

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