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Trigonometry Problem?
A football player stands at a distance c behind the middle of the goal. He sees the angle of elevation of the nearer crossbar to be u and that of the farther one to be v. Show that the distance between the goals is c (tan u cot v - 1).
1 Answer
- Anonymous9 years agoFavorite Answer
Let the length of the pitch be l and the height of the crossbar be h.
Then:
Tan(u) = h/c for the near crossbar
Tan(v) = h/(c+l)
So h = cTan(u) = (c+l)Tan(v)
c(Tan(u) - Tan(v)) = lTan(v)
So l = c(Tan(u)/Tan(v) - Tan(v)/tan(v)) = c (Tan(u)cot(v) - 1)) as required