Question

question 4
10 pts
g.gsr.6.1 (mc)
find the value of x and y.
image of a right triangle with two 45° angles, one leg is √3, hypotenuse is y, the other leg is x
options:
○ x = 3, y = 3√2
○ x = √3, y = √6
○ x = √3, y = 3√2
○ x = 3, y = √6

Explanation:

Step1: Identify Triangle Type

The triangle has a right angle and two \(45^\circ\) angles, so it's a 45-45-90 triangle. In such triangles, the legs are equal, and the hypotenuse is leg \(\times\sqrt{2}\).

Step2: Find \(x\)

The leg opposite \(45^\circ\) (vertical leg) is \(\sqrt{3}\). In a 45-45-90 triangle, the other leg (\(x\)) is equal to this leg. So \(x = \sqrt{3}\).

Step3: Find \(y\) (Hypotenuse)

Using the 45-45-90 ratio, hypotenuse \(y=\text{leg}\times\sqrt{2}\). Substituting the leg (\(\sqrt{3}\)): \(y = \sqrt{3}\times\sqrt{2}=\sqrt{6}\).

Answer:

\(x = \sqrt{3}, y = \sqrt{6}\) (corresponding to the option: \(x = \sqrt{3}, y = \sqrt{6}\))