given right triangle xyz, what is the value of tan(y)?\no $\frac{1}{2}$\no $\frac{sqrt{3}}{3}$\no…
given right triangle xyz, what is the value of tan(y)?\no $\frac{1}{2}$\no $\frac{sqrt{3}}{3}$\no $\frac{sqrt{3}}{2}$\no $\frac{2sqrt{3}}{3}$
Answer
Explanation:
Step1: Identify triangle angles and sides
Right triangle with ∠Z=90°, ∠Y=30°, ∠X=60°, hypotenuse XY=4.
Step2: Determine side lengths using 30-60-90 ratios
Opposite 30° (∠Y): XZ = hypotenuse/2 = 4/2 = 2.
Opposite 60° (∠X): YZ = XZ√3 = 2√3.
Step3: Calculate tan(Y) as opposite/adjacent
tan(Y) = XZ/YZ = 2/(2√3) = 1/√3 = √3/3.
Answer:
B. (\frac{\sqrt{3}}{3})