Question : If $\triangle$DEF is right-angled at E, DE = 15, and $\angle$DFE = 60° then, what is the value of EF?
Option 1: $5\sqrt3$
Option 2: $5$
Option 3: $15$
Option 4: $30$
Correct Answer: $5\sqrt3$
Solution :
Given: DE = 15 and $\angle$DFE = 60°
We know, $\tan\theta$ = $\frac{\text{Perpendicular}}{\text{Base}}$
⇒ $\tan 60° = \frac{DE}{EF} = \sqrt{3}$
⇒ EF = $\frac{DE}{\sqrt{3}}$
⇒ EF = $\frac{15}{\sqrt{3}}$
$\therefore$ EF = $5\sqrt{3}$
Hence, the correct answer is $5\sqrt{3}$.
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