Question

This has to do with Ratios of Special Right Triangles.

Answer 1

Answer:

4√3 / 3.

Step-by-step explanation:

From the properties of trigonometric ratios :

             tan30° = 1 / √3

Here,

   Tangent of 30° =  height / base

                        = x / 4

⇒ tan30° = x / 4

⇒ 1 / √3 = x / 4

⇒ 4 / √3 = x

Dividing as well as multiplying by √3:

⇒ ( 4 / √3 ) ( √3 / √3 ) = x

⇒ ( 4√3 ) / ( √3 * √3 ) = x

⇒ ( 4√3 ) / 3 = x

⇒ 4√3 / 3 = x

  Hence, length of the side x is 4√3 / 3.

Answer 2

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

Let, In right ∆ABC ,

• AB = x
• BC = 4
• <ACB = 30°

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

• Length of AB

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

we know,

$\small\boxed{\sf{\pink{\:\tan \theta\:=\:\dfrac{Perpendicular}{Base}}}} \\ \\ \Large{\underline{\mathfrak{\bf{\red{In\:right\:\triangle\:ABC}}}}} \\ \\ \mapsto\sf{\blue{\:\tan 30^{\circ}\:=\:\dfrac{AB}{BC}\:=\:\dfrac{x}{4}}} \\ \\ \small\sf{\green{\:\left(\tan 30^{\circ}\:=\:\dfrac{1}{\sqrt{3}}\right)}} \\ \\ \mapsto\sf{\:\dfrac{1}{\sqrt{3}}\:=\:\dfrac{x}{4}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{4}{\sqrt{3}}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{4.\sqrt{3}}{3}}$

now, keep value of √3 = 1.732,

$\mapsto\sf{\:x\:=\:\dfrac{4\times 1.732}{3}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{6.928}{3}} \\ \\ \mapsto\sf{\blue{\:x\:=\:2.30\:\:\:\:(Ans.)}}$