Question

Fill in the blanks
A vertical pole stands at a point $O$ on a horizontal ground. $A$ and $B$ are points on the ground $d$ metres apart. The pole subtends angles $\alpha$ and $\beta$ at $A$ and $B$ respectively. $AB$ subtends an angle $\gamma$ at $O$, the height of the pole is ___________.

Answer 1

$OA=h\cot \alpha ,OB=h\cot \beta$
Now from $△OAB$ by cosine formula.
$d^2={OA}^2+{OB}^2-2OA.OB\cos$
$=h^2[{\cot }^2\alpha +{\cot }^2\beta -2\cot \alpha \cot \beta \cos \gamma ]$
$\therefore h=\frac{d}{{{}^2[{\cot }^2\alpha +{\cot }^2\beta -2\cot \alpha \cot \beta \cos \gamma ]}^{1/2}}$