The statements that are true regarding triangle LMN are: NM = x, LM = [tex]x\sqrt{2}[/tex] and tan([tex]45^\circ[/tex]) = 1.
Given :
LN = x
[tex]\rm \angle NLM = 45^\circ[/tex]
[tex]\rm \angle LMN = 45^\circ[/tex]
Solution :
[tex]\rm tan45^\circ = \dfrac{x}{NM}[/tex]
[tex]\rm NM = x[/tex]
[tex]\rm sin45^\circ = \dfrac{x}{LM}[/tex]
[tex]\rm \dfrac{1}{\sqrt{2} } = \dfrac{x}{LM}[/tex]
[tex]\rm LM = x\sqrt{2}[/tex]
[tex]\rm tan45^\circ = 1[/tex]
The statements that are true regarding triangle LMN are: NM = x, LM = [tex]x\sqrt{2}[/tex] and tan([tex]45^\circ[/tex]) = 1.
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https://brainly.com/question/19731462
