Question

7 find the exact value of x and y in the following special right triangle. triangle with angles 30°, 60°, 90° and base 2 x = blank y = blank

Explanation:

Step1: Identify triangle type

It is a 30-60-90 right triangle.

Step2: Label sides

Let the side opposite 30° be $s$, opposite 60° be $s\sqrt{3}$, hypotenuse be $2s$. Here, the side opposite 60° is 2, so $s\sqrt{3}=2$.

Step3: Solve for $s$

$s = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$ (rationalize denominator).

Step4: Find $x$ and $y$

$x$ is opposite 30°, so $x = s = \frac{2\sqrt{3}}{3}$. $y$ is hypotenuse, so $y = 2s = \frac{4\sqrt{3}}{3}$.

Answer:

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