Question

What is Answer for sin45°​

Answer 1

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What is the value of Sin 45°

$\huge \bigstar \underline {\color{pink} \mathfrak{ answer}} \bigstar$

SinA value is Opposite / hypotenuse

here opposite value of 45° is a

and hypotenuse value is √2a

Then, Opposite / hypotenuse = a/√2a

So, Value of Sin 45 is 1/√2

Answer: 1/√2

Answer 2

Answer:

To Find :-

Value of sin45°

Solution :-

Let , ABC be a right angles isosceles triangle in which $\sf\angle ABC$ = 90° and AB = BC

Note :- Refer to attachment .

From geometry,

$\sf\angle ACB = \angle BAC = 45$,

AB = a , then BC = aFrom Pythagoras theorem ,

$\sf (AC)^{2} = (AB)^{2} + (BC)^{2}$

$\sf (AC)^{2} = a^{2} + a^{2}$

$\sf (AC)^{2} = 2a^{2}$.

Applying square root on both sides we get :-

AC = $\sf\sqrt{2a^{2}}$$= \sqrt{2}a$

From ∆ABC ,

$\sf\angle A = 45$ ,

we get :-

sin45° = $\dfrac{1}{root2}$

= $\frac{a}{ \sqrt{2}a}$

= $\frac{1}{ \sqrt{2} }$

$\sf\therefore sin45 = \dfrac{1}{\sqrt{2}}$