Question

Given right triangle XYZ, what is the value of tan(Y)?

A. 1/2
B. √3/3
C. √3/2
D. 2√3/3

Answer 1

Option B. √3/3

Explanation:

In a right triangle, the angles are in the ratio,

30° , 60° and 90° then their sides are in the ratio, 1 : √3 : 2

To find the sides XZ and ZY

<Y : <X : <Z = 30° : 60° : 90° and XY = 4

Therefore ,

XZ : ZY : XY = 1 :√3 : 2 = 2 : 2√3 : 4

To find tan(Y)

tan(y) = Opposite side /Adjacent side

tan(y) = XZ/ZY = 2/2√3 = 1/√3 = √3/3

tan(y) = √3/3

Therefore the correct answer is Option B. √3/3

Answer 2

Answer: OPTION B

Explanation:

You must find the value of XZ as following:

`sin(30\°)=XZ/4\\XZ=4*sin(30\°)\\XZ=2`

You must calculate the value of YZ as following:

`cos(30\°)=YZ/4\\YZ=4*cos(30\°)\\YZ=2√(3)`

Now, you can calculate the value of tan(Y), then you obtain:

`tan(Y)=opposite/adjacent\\tan(Y)=2/2√(3)`

When you rationalized the expresion, you obtain:

`(2)/(2√(3))*(2√(3))/(2√(3))=(4√(3))/(4*3)=(√(3))/(3)`

`tan(Y)=(√(3))/(3)`