Multiple choice

If the angle of elevation of sun is $\displaystyle \theta $ and the length of the shadow of a pole of length is $s$, then

  1. $\displaystyle p=s\cos \theta $
  2. $\displaystyle p=s\sin \theta $
  3. $\displaystyle p=\frac{s}{\cot \theta }$
  4. $\displaystyle p=s \cot \theta $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the right triangle formed by the pole and its shadow, tan(theta) = p/s. Rearranging gives p = s tan(theta) = s/cot(theta). Thus option C is correct.

AI explanation

The angle of elevation of the sun forms a right triangle where the pole of length p is the opposite side and the shadow of length s is the adjacent side. The tangent of the angle theta is the ratio of the opposite side to the adjacent side, so tan theta equals p divided by s. Since cot theta is the reciprocal of tan theta, we can write cot theta equals s divided by p. Multiplying both sides by p and dividing by cot theta gives the formula p equals s divided by cot theta.

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