Question

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Answer 1

Step-by-step explanation:

Given: Figure

To find:

$\frac{cot \: y°}{cot \: x°}$

Solution:

We know that in right triangle,we can apply co-tangent

$cot\theta=\frac{Base}{Perpendicular}$

Step1: Write cot y°

In ∆ACB

$cot\:y°=\frac{AC}{BC}...eq1$

Step 2: Write cot x°

In ∆ADC

$cot\:x°=\frac{AC}{DC}...eq2$

Step 3: Divide both eq1 and eq2

$\frac{cot \: y°}{cot \: x°} =\frac{AC}{BC} \times \frac{DC}{AC} \\ \\\frac{cot \: y°}{cot \: x°} = \frac{DC}{BC} \\ \\ \\\frac{cot \: y°}{cot \: x°} = \frac{DC}{2DC} \\ \\\frac{cot \: y°}{cot \: x°} = \frac{1}{2}$

Final answer:

$\bold{\red{\frac{cot \: y°}{cot \: x°} = \frac{1}{2}}}$

Option B is correct.

Hope it helps you.

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