Question

question 8
10 pts
g.gsr.6.1 (mc)
find the value of x and y.
image of a right triangle with 30° angle, hypotenuse y, one leg 8√3, the other leg x
options:
○ x = 8, y = 16
○ x =8, y = 12
○ x = 4, y = 4√3
○ x = 4, y = 8

Explanation:

Step1: Identify Triangle Type

This is a 30-60-90 right triangle. In such a triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\) (opposite 30°, 60°, 90° respectively). The side adjacent to 30° (with length \(8\sqrt{3}\)) is opposite 60°, so it's the \(\sqrt{3}\) part.

Step2: Find x (opposite 30°)

Let the side opposite 30° be \(x\), adjacent (opposite 60°) be \(8\sqrt{3}\), hypotenuse \(y\). From the ratio, \(\frac{x}{1}=\frac{8\sqrt{3}}{\sqrt{3}}\). Simplify: \(x = 8\).

Step3: Find y (hypotenuse)

Hypotenuse is twice the side opposite 30°, so \(y = 2x = 2\times8 = 16\).

Answer:

A. \(x = 8, y = 16\)