Respuesta :

luisejr77

Answer: second option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]

imlittlestar

Answer:

The correct answer is second option

6√2

Step-by-step explanation:

From the figure we can see a right angled triangle, with angles 45°, 45° and 90°

The height of triangle is 6 units

Points to remember

If the angles of a right angled triangle are  45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2

To find the value of x

From the figure we can see that, the angles are  45°, 45° and 90°

Therefore the two sides are equal and one side is x

The equal side is 6 units

Therefore 6 : 6 : x = 6 : 6 : 6√2

The value of x = 6√2

The second option is the correct answer.

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