Question

given right triangle gyk, what is the value of \\(\tan(g)\\)?

\\(\sqrt{3}\\)

\\(\frac{2\sqrt{3}}{3}\\)

\\(\frac{\sqrt{3}}{2}\\)

\\(\frac{1}{2}\\)

Explanation:

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<reasoning>

Identify the target angle and given values

\[

$$\begin{aligned} &\angle G = 60^\circ\\ &\angle Y = 30^\circ\\ &\angle K = 90^\circ \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(G) = \tan(60^\circ) = \sqrt{3}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\sqrt{3}\)</mcq-correct>
<mcq-option>(B) \(\frac{2\sqrt{3}}{3}\)</mcq-option>
<mcq-option>(C) \(\frac{\sqrt{3}}{2}\)</mcq-option>
<mcq-option>(D) \(\frac{1}{2}\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the target angle and given values

\[

$$\begin{aligned} &\angle G = 60^\circ\\ &\angle Y = 30^\circ\\ &\angle K = 90^\circ \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(G) = \tan(60^\circ) = \sqrt{3}
\]
</reasoning>

<answer>
<mcq-correct>(A) \(\sqrt{3}\)</mcq-correct>
<mcq-option>(B) \(\frac{2\sqrt{3}}{3}\)</mcq-option>
<mcq-option>(C) \(\frac{\sqrt{3}}{2}\)</mcq-option>
<mcq-option>(D) \(\frac{1}{2}\)</mcq-option>
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