Question

Need help on trigonometry again​

Answer 1

`\fbox{3√(2)}`
`3\sqrt2`

Explanation:

Step 1:

Let us figure out the measurements of all the angles first. We are given one angle of 45º, and another of 90º. The angles of a triangle must add up to 180º, hence we can use basic addition and subtraction to find the last angle.

`\angle=180-90-45\\\angle=45`

Great our angle is 45º! Notice something...?

Step 2:

We now have two 45º angles in our triangle. This means we have an isosceles triangle.

According to BATh (base angle theorem), in an isosceles triangle, the angles opposite the congruent sides are congruent. Thus, y is congruent to the given side of
`3\sqrt2`.

y=
`\fbox{3√(2)}`
`3\sqrt2`

I hope this helps! Let me know if you have any questions :)