Question

2
find the exact value of x and y in the
following special right triangle.

x =

y =

Explanation:

Step1: Identify triangle type

30-60-90 right triangle, sides ratio $1:\sqrt{3}:2$

Step2: Relate given side to ratio

Adjacent to 60°: 2 = longer leg = $\sqrt{3} \times$ shorter leg

Step3: Find shorter leg (x)

$x = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$

Step4: Find hypotenuse (y)

$y = 2x = 2 \times \frac{2\sqrt{3}}{3} = \frac{4\sqrt{3}}{3}$

Answer:

$x = \frac{2\sqrt{3}}{3}$, $y = \frac{4\sqrt{3}}{3}$