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MathNet 2008-part-03 — 165 problems (EN–VI) Question 137

Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)

Question 137

A pole broke at a height of $4.2~\mathrm{m}$ above the ground at an angle of $79^\circ$ (see the figure).
Question illustration
What was the height of the pole before it broke? How many $\mathrm{dm}^3$ of wood does the lower part of the pole, up to the break, contain, if the diameter of the pole is $60~\mathrm{cm}$?