Multiple choice

From the top of the tree, a man observes the angle of depression of a point which is at a distance of $40\ m$ from the foot is $75^{0}$. The height of the tree is :

  1. $40\sqrt{3}\ m$
  2. $40(2+\sqrt{3})\ m$
  3. $21\sqrt{3}\ m$
  4. $3\sqrt{21}\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Height h = 40 * tan(75 degrees). tan(75) = tan(45+30) = (1 + 1/sqrt(3)) / (1 - 1/sqrt(3)) = (sqrt(3)+1)/(sqrt(3)-1) = (sqrt(3)+1)^2 / 2 = (3+1+2sqrt(3))/2 = 2 + sqrt(3). Height = 40(2 + sqrt(3)).

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