A new coffee shop is being built. Its location is the reflection of the arcade's coordinates across the y-axis. Which procedure will find the correct distance between the arcade and
the new coffee shop?
A Find the sum of 31 and 3).
B Simplify the expression|-5] + [5].
C Find the distance between (5,3) and (5, -3).
D Find the distance of each point from the y-axis and then subtract.

d

Step-by-step explanation:

SOH CAH TOA

Step-by-step explanation:

Finding sides (first 2 pictures)

For finding sides of a triangle, you first must "map" the triangle using the given angle as a reference. In this case (for the first picture) use the angle with the measure of 32. The side directly across from the reference angle is the opposite. Label it "O." The side directly across from the right angle is the hypotenuse. Label it "H." Thus, the other side (12) must be the adjacent side. Label it "A." Since you are given and , and you know that is the hypotenuse and is the adjacent side, you use the CAH operation, meaning .

Set it up like so:

Use order of operations:

Plug that in your calculator and that's your answer.

Finding angles (last 3 pictures)

In the third picture, you are given two sides and x. When finding angles, you  only use what you are given. However, instead of using sin, cos, tan, you must use the inverse, which is and so on.

Since you are trying to find x, you still use it as your reference angle. 20 is the hypotenuse and 11 is adjacent. Don't worry about the other side- it's not necessary unless it's given. Since you are given the hypotenuse and the adjacent, you use the property. (inverse)

It's done like so:

Put that in your calculator, and that's the answer! The rest of the angle problems are done the same way, just using different sides.