Answer:
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Step-by-step explanation:
Find the diagram attached.
From the right triangle XYZ:
XY is the hypotenuse
XZ and YZ are opposite and adjacent
To get value of tan(Y), we will use the SOH, CAH, TOA, trigonometry identity.
According to TOA:
Tan(Y) = XZ/ZY
First let us get XZ
Using SOH
SinY = opp/hyp = XZ/XY
SinY = XZ/4
Sin30 = XZ/4
XZ = 4sin30
XZ = 4(0.5)
XZ = 2units
Next is to get ZY:
Using Pythagoras theorem:
ZY²+XZ² = XY²
ZY² = XY²-XZ²
ZY² = 4²-2²
ZY² = 16-4
ZY² = 12
ZY = √12
ZY = √4*3
ZY = 2√3
Solve for tan(Y):
Since Tan(Y) = XZ/ZY
Tan(Y) = 2/2√3
Tan(Y) = 1/√3
Rationalize
Tan(Y) = 1/√3*√3/√3
Tan(Y) = √3/√9
Tan(Y) = √3/3
Hence the correct option is A. StartFraction StartRoot 3 EndRoot Over 3 EndFraction
