Question

given right triangle xyz, what is the value of tan(y)? - o 1/2 o √3/3 o √3/2 o 2√3/3

Explanation:

Step1: Identify angle Y

Angle Y = 30° (sum of angles: 180°-90°-60°=30°).

Step2: Define tan(Y)

tan(Y) = opposite/adjacent (trigonometric ratio).

Step3: Determine sides for Y

Opposite to Y: XZ; adjacent to Y: YZ. Hypotenuse XY=4.

Step4: Use 30-60-90 ratio

Hypotenuse=2k=4 ⇒ k=2. XZ=k=2 (opposite 30°), YZ=k√3=2√3 (opposite 60°).

Step5: Calculate tan(Y)

tan(Y)=XZ/YZ=2/(2√3)=1/√3=√3/3 (rationalized).

Answer:

B. √3/3