Question

Find the value of x & y
y
12
30

Answer 1

x =
`(√(12) )/(3)`12 = 8
`√(3)`

y =
`(√(3) )/(3)`12 = 4
`√(3)`

Let me know if you need some help simplifying the expressions or o the trig side of things

Explanation:

I'm not sure if this is full out trig or recognizing special triangles, specifically 30-60-90 triangles. Of course since one angle is 30 degrees and the other is 90 degrees this is a 30-60-90 triangle.

with 30-60-90 tringles the basic guide is as follows.

The three legs will be referred to as the hypotenuse, short leg and long leg. I will use H, S and L.

H = 2S =
`(√(12) )/(3)`L

S = .5H =
`(√(3) )/(3)`L

L =
`(√(3) )/(2)`H = S
`√(3)`

If this is trig just break out the unit circle and SOH CAH TOA

So x is the hypotenuse, and y is the short leg and we know the long leg is 12, so we can use that.

to find the hypotenuse knowing the long leg we use H =
`(√(12) )/(3)`L and to find the short leg with the long leg you use S =
`(√(3) )/(3)`L. now just plug in 12 for L