Answer:
[tex]x=\dfrac{3}{2}[/tex]
[tex]y =\dfrac{\sqrt{3}}{2}[/tex]
[tex]\newline[/tex]
Step-by-step explanation:
[tex]\newline[/tex]
In a special 30-60-90 right triangle, the lengths of its sides are in the ratio 1 : √3 : 2, which means that:
- The hypotenuse is twice the length of the shortest leg.
- The longest leg (opposite the 60° angle) is √3 times the length of the shortest leg.
[tex]\newline[/tex]
In the given triangle, the hypotenuse measures √3. Therefore, the length of the shortest leg (opposite the 30° angle) is:
[tex]\newline[/tex]
[tex]y =\dfrac{\sqrt{3}}{2}[/tex]
[tex]\newline[/tex]
The longest leg is √3 times the length of the shortest leg. Therefore:
[tex]\newline[/tex]
[tex]x=\sqrt{3} \cdot y[/tex]
[tex]x=\sqrt{3} \cdot \dfrac{\sqrt{3}}{2}[/tex]
[tex]x=\dfrac{\sqrt{3} \cdot \sqrt{3}}{2}[/tex]
[tex]x=\dfrac{3}{2}[/tex]
