Question

Find the value of y.

Answer 1

Answer: Second option.

Explanation:

By the Right Triangle Altitude Theorem, we know that the altitude "h" (Observe the figure attached) is:

`h=√(9*3)\\h=3√(3)`

Then, since we know the value of the altitude, we can calculate the value of "y" with the Pythagorean Theorem:

`a=√(b^2+c^2)`

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

We can identify that:

`a=y\\b=9\\c=h=3√(3)`

Then, substituting values, you get that "y" is:

`y=\sqrt{9^2+(3√(3))^2}=6√(3)`