Find the altitude of an equilateral triangle of side 8 cm.
\(4\sqrt{3}\,\text{cm}\)
Step 1: In an equilateral triangle, all three sides are equal and all angles are 60°.
Step 2: The altitude (height) of an equilateral triangle divides it into two equal right-angled triangles.
Step 3: Formula for altitude of an equilateral triangle is:
\[ h = \dfrac{\sqrt{3}}{2} \times a \]
where \(a\) = length of each side.
Step 4: Here, \(a = 8\,\text{cm}\).
So,
\[ h = \dfrac{\sqrt{3}}{2} \times 8 \]
Step 5: Simplify:
\[ h = 4\sqrt{3}\,\text{cm} \]
Final Answer: The altitude is \(4\sqrt{3}\,\text{cm}\).