Question

5
find the exact value of x and y in the
following special right triangle.
(image of a right triangle with angles 30°, 60°, 90°, the side opposite 30° is 2, the other leg is x, the hypotenuse is y)
x =
y =

Explanation:

Step1: Identify triangle type

It's a 30-60-90 right triangle.

Step2: Relate sides to angles

The side opposite 30° is half the hypotenuse; side opposite 60° is $\sqrt{3}$ times the side opposite 30°.

Step3: Find x (opposite 30°)

Let side opposite 30° = $x$, side opposite 60° = 2. So $2 = x\sqrt{3} \Rightarrow x = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$.

Step4: Find y (hypotenuse)

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

Answer:

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