Altitude of an equilateral triangle with side 33 cm (repaired options):\nFind the exact length of the altitude (height) of an equilateral triangle whose side is 33 cm.

Introduction / Context:
(Recovery–First applied) The original options (4.5, 3.5, 2.5, 6.5) were inconsistent with an equilateral triangle of side 33 cm. The correct altitude formula is well-known, so we minimally repair the options to include the exact expression and a sensible approximation.

Given Data / Assumptions:

• Equilateral triangle side s = 33 cm.
• Altitude h = (√3/2) * s.

Concept / Approach:
Altitude in an equilateral triangle splits it into two 30–60–90 right triangles; the height equals (√3/2) times the side length.

Step-by-Step Solution:

Verification / Alternative check:
Use Pythagoras in the half-triangle: (33/2)^2 + h^2 = 33^2 → h^2 = 33^2 − (16.5)^2 = (33 − 16.5)(33 + 16.5) = 16.5 * 49.5 = 816.75 → h ≈ 28.6 cm, consistent with 33√3/2.

Why Other Options Are Wrong:
24.0 cm, 19.1 cm, 16.5 cm do not match the exact altitude formula; 28.6 cm is the rounded value, while 33√3 / 2 cm is exact.

Common Pitfalls:
Confusing altitude with medians in non-equilateral triangles; here all coincide and the altitude formula is precise.

Final Answer:
33√3 / 2 cm