Question

Tower $PQ$ subtends an angle $\alpha$ at a point $A$on the same level as the foot $Q$ of the tower. It also subtends the same angle $\alpha$ at a point $B$ where $AB$ subtends the angle $\alpha$ with $AP$ then:

• A. $AB=BO$
• B. $BO=2AO$
• C. $\frac{AB}{BQ}=\frac{1}{2}$
• D. none of these

Answer 1

The correct option is C $\frac{AB}{BQ}=\frac{1}{2}$

From Figure,

$\angle A=\angle B=\alpha$

Since the line $AB$ subtends an angle $\alpha$ with $PQ$

The $\Delta PAB$ is Equilateral Triangle.

$PQ$ is perpendicular bisector .

$⟹\frac{AB}{BQ}=\frac{1}{2}$