Question

from the figure find the value of PQ​

Answer 1

Step-by-step explanation:

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Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• QB = d
• AB = h

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• PQ = ?

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

We know,

$\small\boxed{\sf{\pink{\:\tan \theta\:=\:\dfrac{Perpendicular}{Base}}}}$

$\Large{\underline{\mathfrak{\bf{In\:\triangle\:AQB}}}}$

$\small{\boxed{\sf{\pink{\:\tan 60^{\circ}\:=\:\dfrac{AB}{QB}\:=\:\dfrac{h}{d}}}}} \\ \\ \small\sf{\green{\:\:\:\:\:\left(\tan 60^{\circ}\:=\:\sqrt{3}\right)}} \\ \\ \mapsto\sf{\:\sqrt{3}\:=\:\dfrac{h}{d}} \\ \\ \mapsto\sf{\pink{\:h\:=\:d\sqrt{3}....(1)}}$

Again,

$\Large{\underline{\mathfrak{\bf{In\:\triangle\:APB}}}}$

$\small{\boxed{\sf{\pink{\:\tan 30^{\circ}\:=\:\dfrac{AB}{PB}\:=\:\dfrac{h}{PQ+d}}}}} \\ \\ \small\sf{\green{\:\:\:\:\:\left(\tan 30^{\circ}\:=\:\dfrac{1}{\sqrt{3}}\right)}} \\ \\ \mapsto\sf{\:(PQ+d)\:=\:h\sqrt{3}}$

keep value by equ(1) ,

$\mapsto\sf{\:(PQ+d)\:=\:\sqrt{3}\times d\sqrt{3}} \\ \\ \mapsto\sf{\:PQ\:=\:3d\:-\:d} \\ \\ \mapsto\boxed{\sf{\orange{\:PQ\:=\:2d\:\:\:\:\:\:Ans.}}}$

$\Large{\underline{\mathfrak{\bf{Thus:-}}}}$

• Value of PQ = 2d.