Multiple choice

If the angles of elevaton of the top of a tower from two points distance s and t $\displaystyle \left ( s> t \right )$ from its foot are $\displaystyle 30^{0}$ and $\displaystyle 60^{0}$ respectively then the height of the tower is

  1. $\displaystyle \sqrt{s+t}$
  2. $\displaystyle \sqrt{st}$
  3. $\displaystyle \sqrt{s-t}$
  4. $\displaystyle \sqrt{\frac{s}{t}}$
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B Correct answer
Explanation

Let h be the height. tan(30) = h/s => h = s * tan(30) = s / sqrt(3). tan(60) = h/t => h = t * tan(60) = t * sqrt(3). Thus h^2 = (s / sqrt(3)) * (t * sqrt(3)) = st. So h = sqrt(st).

AI explanation

Let h be the height of the tower, with tan 30 degrees equaling h over s and tan 60 degrees equaling h over t. Since tan 30 degrees is 1 over the square root of 3 and tan 60 degrees is the square root of 3, we have h equals s divided by the square root of 3 and h equals t multiplied by the square root of 3. Multiplying these two expressions for h yields h squared equaling st. Therefore, the height of the tower is the square root of st.

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