Question

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

Answer 1

Answer:

Option B.  √3/3

Step-by-step 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

Step-by-step 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:

$cos(30\°)=YZ/4\\YZ=4*cos(30\°)\\YZ=2\sqrt{3}$

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

$tan(Y)=opposite/adjacent\\tan(Y)=2/2\sqrt{3}$

When you rationalized the expresion, you obtain:

$\frac{2}{2\sqrt{3}}*\frac{2\sqrt{3}}{2\sqrt{3}}=\frac{4\sqrt{3}}{4*3}=\frac{\sqrt{3}}{3}$

$tan(Y)=\frac{\sqrt{3}}{3}$