Multiple choice

In a cubical hall $ABCDPQRS$ with each side $10m,\ G$ is the center of the wall $BCRQ$ and $T$ is the mid point of the side $AB$. The angle of elevation of $G$ at the point $T$ is

  1. $\displaystyle \sin^{-1}(\frac{1}{\sqrt{3}})$
  2. $\displaystyle \cos^{-1}(\frac{1}{\sqrt{3}})$
  3. $\displaystyle \tan^{-1}(\frac{1}{\sqrt{3}})$
  4. $\displaystyle \cot^{-1}(\frac{1}{\sqrt{3}})$
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A Correct answer
Explanation

In a cube of side 10, let T be (5, 0, 0) and G be (10, 5, 5). The vector TG = (5, 5, 5). The projection on the floor is (5, 5, 0) with length sqrt(50). The height is 5. Tan(theta) = 5 / sqrt(50) = 1/sqrt(2). The angle is sin^-1(1/sqrt(3)).

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