Question

HELP!!!
Find x.
A. 9
B. 9 times the square root of 2
C. 4 point 5 times the square root of 2
D. 18 times the square root of 2

Answer 1

Can I walk you through this problem?

Answer 2

go ahead

Answer 3

The 90 degree angle is directly across from the side value of 18. This means that you should associate the 90 degree angle with 18.

The 45 degree angle is across from a different side angle, but we don't have to care about that because it isn't across from the x, and the x is what we care about.

So, find the angle that is across from the x so that we know what corresponds with the x. (This is just like how the 18 corresponds with the 90 degree angle)

The angle that corresponds with the x is unknown, but it's easy to figure out. A triangle is equal to 180 degrees, so to find the missing angle, think 180=45+90+a. The missing value is 45, so the x value corresponds with a 45 degree angle.

I'm pretty sure you're dealing with sin, so I'll use that to solve.

The equation is \[\sin45/x=\sin90/18\]

This is in the form (sin of one angle)/(side value (which is x in this case))/(sin of a different angle)/(side value (which is 18 in this case))

From there, you get (sin45)(18)=(sin90)(x)

The sin of 90 is 1 and the sin of 45 is 0.7071, so you get:

x=12.728

This is the value of x in the problem.

Answer 4

if that's the answer then that is not one of the multiple choice question

Answer 5

How have you been solving these, with sin or without?

Answer 6

Just kidding. The answer should be 9. I'll explain that in a second. We solve it way differently in Pre-Calc.

Answer 7

without and ok

Answer 8

Okay, here it is. This is what's called a 45-45-90 triangle. For the values of the sides of a 45-45-90 triangle, think of it like this. The side for a 45 degree angle is x. The side for the other 45 degree angle is also x. The side for the 90 degree angle is just double that, so it's 2x. So, the side for the 90 degree angle is 18. This means that this side value is double the side value of the 45 degree angle. So, 18 divided by 2 is 9, which is your answer.