Question

HELP Geometry does anyone know this

Answer 1

The correct answer is second option

6√2

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.

Answer 2

Answer: second option.

Explanation:

You need to remember the following identity:

`sin\alpha=(opposite)/(hypotenuse)`

In this case, we can observe that:

`\alpha=45\°\\opposite=6\\hypotenuse=x`

Now you must substitute these values into
`sin\alpha=(opposite)/(hypotenuse)` and solve for the hypotenuse. Then:

`sin(45\°)=(6)/(x)\\\\(x)(sin(45\°))=6\\\\x=(6)/(sin(45\°))\\\\x=6√(2)`