Answer:
Step-by-step explanation:
here is how you find the answer
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
now apply the above rules to the given triangle
where we are given the angle of 30° and the Adj side of 27
y is the Hyp of this triangle and x is the Opp side of this triangle, now plug in the given values as follows
so use CAH Cos(30) = 27 / Hyp
Hyp = 27 / Cos(30)
Hyp = 27 / ([tex]\sqrt{3}[/tex] / 2)
Hyp = 27 * 2 / [tex]\sqrt{3}[/tex]
Hyp = 54 / [tex]\sqrt{3}[/tex]
y = 54 / [tex]\sqrt{3}[/tex]
use SOH, since we know the exact value for the Hyp from above
Sin(30) = Opp / ( 54 / [tex]\sqrt{3}[/tex] )
Sin(30) * 54 / [tex]\sqrt{3}[/tex] = Opp
1/2 * 54 / [tex]\sqrt{3}[/tex] = Opp
27 / [tex]\sqrt{3}[/tex] = Opp
x = 27 / [tex]\sqrt{3}[/tex]
:)
