Question

$<b>$Find the value of sin30° geometrically . with help of diagram ?

Answer 1

Let ABC be an equilateral triangle.

In equilateral triangle, each angle equals to 60° and all sides are equal.

Suppose each side be 2a.

Now, Draw a perpendicular AD from the vertex A to side BC.

In ∆ ABD and ∆ ACD

∠ADB = ∠ADC ( as both are 90° )

AB = BC ( all sides are equal in equilateral triangle )

AD = AD ( Common )

•°• ∆ ABD ≅ ∆ ACD ( By RHS congruency rule )

Now, BD = DC ( By CPCT )

Also, ∠BAD = ∠CAD

Now, ∠BAD = ∠CAD = ( 1 / 2 ) ∠BAC = ( 1 / 2 ) × 60° = 30°

Side BC = 2a

BD = DC = ( 1 / 2 ) BC = ( 1 / 2 ) 2a = a

Now,

In ∆ ABD

sin 30° = BD / AB = a / 2a = 1 / 2

Hence proved.