Let AB be the pole and its shadow is BC. According to the question,
Shadow of the pole =√3 height of the pole ⇒‌‌BC=√3‌AB . . . (i) Now, let angle of elevation of Sun is θ. Then, in △ABC, ‌tan‌θ‌=‌
AB
BC
⇒tan‌θ‌=‌
AB
√3‌AB
‌‌[‌ from Eq. (i)] ‌ ⇒‌tan‌θ‌=‌