Question

Use the diagram to complete the statement

Answer 1

Answer:
`BC=4√(2)`

Explanation:

For this exercise you need to analize the diagram given in the exercise.

You can see that the triangle BCG is a Right triangle, because it has an angle that measures 90 degrees.

Then, you need to use the following Trigonometry Identity:

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

In this case you can identify that:

`\alpha=45\°\\\\opposite=CG=4\\\\hypotenuse=BC`

Now, you must substitute those values into
`sin\alpha=(opposite)/(hypotenuse)`, as below:

`sin(45\°)=(4)/(BC)`

And finally, you must solve for BC in order to find its value.

Then, you get that this is:

`(BC)(sin(45\°))=4\\\\BC=(4)/(sin(45\°))\\\\BC=4√(2)`