Question

take any triangle prove sin30=1/2 sin 90=1

Answer 1

Hii friend,

Let ∆ABC be a right angled triangle.

In which,

angle B = 90° and angle A = 45°

CLEARLY,

Angle C = 45°.

THEREFORE,

Angle A= Angle C

AB = BC

LET,

AB = BC = a units .

THEN,

AC = Under root AB²+BC² = ✓ a²+a² = ✓2a² = ✓2 a units.

Base AB = a , Perpendicular BC = a , Hypotenuse AC = ✓2 a.

THEREFORE,

Sin45° = P/H = BC/AC = a/✓2a = 1/✓2......PROVED...

Consider an equilateral triangle ABC with side equal to 2a.

Then,

Each angle of a triangle ABC is 60°.

From A, draw AD Perpendicular to BC

Then,

Clearly Angle ADB = 90°

And ,

Angle BAD = 30°.

From a right angled triangle ADB , we have

AD = ✓ AB²- BD² = ✓(2a)² - a² = ✓4a²-a² = ✓3a² = ✓3 a.

IN RIGHT ANGLED TRIANGLE ADB , WE HAVE

Base BD= a , Perpendicular AD = ✓3a and Hypotenuse AB = 2a.

THEREFORE,

Sin30° = P/H = BD/AB= a/2a = 1/2.... proved...


PROVED Sin90° = 1, by the given hints...
ITS YOUR HOMEWORK..



HOPE IT WILL HELP YOU... :-)