Question

From the top of a pole of height h, the angle of elevation of the top of the tower is $\alpha$. The pole subtends an angle $\beta$ at the top of the tower. The height of the tower is____

Answer 1

H = $\frac{hsin\alpha cos(\alpha -\beta )}{sin\beta }$
OA = H cot $\alpha$, BM = (H - h) tan $({90}^0-\alpha +\beta )$
$\therefore$ H cot $\alpha$ = (H - h) cot $(\alpha -\beta )$
$\therefore$ H[cot ($\alpha$ - $\beta$) - cot $\alpha$] = h cot cot $(\alpha -\beta )$.
Change to sin and cos.