Question

The length of an altitude of an equilateral triangle of side $a$ is:

• A. $\frac{2a}{\sqrt{3}}$
• B. $\frac{\sqrt{3}}{2a}$
• C. $\frac{a\sqrt{3}}{2}$
• D. $\frac{a}{2\sqrt{3}}$

Answer 1

The correct option is C $\frac{a\sqrt{3}}{2}$

Each angle of equilateral $△$ is ${60}^{\circ }$ .

$\Rightarrow \angle B={60}^{\circ }$

Let $AD$ be the altitude.

Now in $△ABD$, we have

$\frac{AD}{AB}=\sin {60}^{\circ }$

$\Rightarrow \frac{AD}{a}=\frac{\sqrt{3}}{2}\Rightarrow AD=\frac{\sqrt{3}}{2}a$