Question

which statements are true regarding triangle lmn? check all that apply. □ nm = x □ nm = x√2 □ lm = x√2 □ tan(45°) = √2/2 □ tan(45°) = 1

Explanation:

Step1: Recall tangent of 45 - degree

$\tan(45^{\circ}) = 1$

Step2: Analyze right - triangle properties

In right - triangle LMN with $\angle L = 45^{\circ}$ and $\angle N=90^{\circ}$, $\angle M = 45^{\circ}$, so it is an isosceles right - triangle. Let $NM = x$, then $LN=x$ and by Pythagorean theorem $LM=\sqrt{x^{2}+x^{2}}=x\sqrt{2}$

Answer:

$\tan(45^{\circ}) = 1$, $LM = x\sqrt{2}$, $NM = x$