Question

1.
part a: using <w as the reference angle, what is the exact tangent ratio for ▲wkv? do not simplify.
part b: by using <w as a reference angle, compare the ratios of the triangle wkv and eki?

ie	16	iv	38.4
ik	38.4	we	41.6
ke	41.6	wv	32

Explanation:

Step1: Define tangent ratio

For angle $\angle W$, $\tan(\angle W) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Identify sides for $\triangle WKV$

Opposite side to $\angle W$ is $VK = VI + IK = 38.4 + 38.4$, adjacent side is $WV = 32$. So $\tan(\angle W) = \frac{VK}{WV} = \frac{38.4+38.4}{32}$

Step3: Analyze $\triangle EKI$ tangent

For $\angle W$ (corresponding angle to $\angle E$ in similar triangles), $\tan(\angle E) = \frac{IK}{IE} = \frac{38.4}{16}$

Step4: Simplify and compare ratios

Simplify $\frac{38.4+38.4}{32} = \frac{76.8}{32} = 2.4$, and $\frac{38.4}{16} = 2.4$. The ratios are equal.

Answer:

Part A: $\frac{VK}{WV}$ or $\frac{38.4+38.4}{32}$
Part B: The tangent ratios are equal.