Question

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

Answer 1

`(13)/(√(2))` or 9.19 (approximately). I am confused how the question is asking for it to be typed, so it might be this:
`(13)/(√(2))` , but if you cannot type that in, then maybe it is sin(45) * 13.

Explanation:

The three main trigonometric ratios are: sine (o/a), cosine (a/h), or tangent (o/a) depending on the given. To help you remember them, you can use the saying SOH CAH TOA, which is sin = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent.

In this problem, we are going to use one that has the hypotenuse, which rules out tangent, and leaves us with sine or cosine. Since, we are given the hypotenuse and the opposite side (from angle 45), we will be using sine. Then we just need to set up the trigonometric ratio:

sin (45) = x/13

Then, you need to get x by itself, so you multiply 13 on each side, which leaves you with:

x = sin(45) * 13 = 9.19 (approximately)

This could also be seen as a special right triangle, where the hypotenuse is
`x√(2)`, and the two sides are x.

So, to find the value of x, you could also do this: 13/
`√(2)`, which might be how the question wants it formatted.

Good luck!