Question

deriving a tangent ratio for special triangles
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: Identify triangle type

Triangle LMN is a 45-45-90 right triangle (right angle at N, two 45° angles), so it is isosceles with legs LN = NM.

Step2: Confirm leg length

Given $LN = x$, so $NM = x$.

Step3: Calculate hypotenuse length

In 45-45-90 triangles, hypotenuse = leg $\times \sqrt{2}$. Thus $LM = x\sqrt{2}$.

Step4: Calculate $\tan(45^\circ)$

Tangent = $\frac{\text{opposite}}{\text{adjacent}}$. For 45°, $\tan(45^\circ) = \frac{x}{x} = 1$.

Answer:

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