Question

ln the given fig ,AB perpendicular to BC, DC perpendicular to BC,BD perpendicular to AC ,<D=30° and DC=60√3 m.Find the length of AB.​

Answer 1

Step-by-step explanation:

∠BDC = 30°

And DC = 60√3 m

In △DCB ,

$\rm \dashrightarrow tanθ = \dfrac{Opposite \: side}{Adjacent \: side}$

$\rm \dashrightarrow tan 30^{\circ} = \dfrac{BC}{DC}$

$\rm \dashrightarrow \dfrac{1}{\sqrt{3}} = \dfrac{BC}{60\sqrt{3}}$

$\rm \dashrightarrow \dfrac{60\sqrt{3}}{\sqrt{3}} = BC$

$\rm \dashrightarrow BC = 60m$

In △ABC,

∠ABC = 90°, ∠BAC = 60° , ∠ACB = 30°

$\rm \dashrightarrow tanθ = \dfrac{Opposite \: side}{Adjacent \: side}$

$\rm \dashrightarrow tan 30^{\circ} = \dfrac{AB}{BC}$

$\rm \dashrightarrow \dfrac{1}{\sqrt{3}} = \dfrac{AB}{60}$

$\rm \dashrightarrow \dfrac{60}{\sqrt{3}} = AB$

$\rm \dashrightarrow \dfrac{60}{\sqrt{3}} \times \dfrac{ \sqrt{3} }{ \sqrt{3} } = AB$

$\rm \dashrightarrow \dfrac{60 \sqrt{3} }{3} = AB$

$\rm \dashrightarrow AB = 20\sqrt{3}$

$\dashrightarrow \underline{\boxed{\rm Length \: of \: AB = 20\sqrt{3}m}}$

Answer 2

Step-by-step explanation:

hope it will help full for you