Answer:
[tex]\large\boxed{1.\ x=10,\ y=10\sqrt3}\\\boxed{2.\ x=15,\ y=10\sqrt3}[/tex]
Step-by-step explanation:
Look at the pictures.
1.
We have the triangle 30° - 60° - 90°. The sides are in proportion 1 : √3 : 2.
Therefore:
[tex]x=\dfrac{20}{2}=10,\ y=10\sqrt3[/tex]
2.
We have the triangle 30° - 60° - 90°. The sides are in proportion 1 : √3 : 2 and the triangle 45° - 45° - 90°. The sides are in proportion 1 : 1 : √2.
Therefore:
[tex]x=\dfrac{30}{2}=15[/tex]
The common side of the green and pink triangle also has a length of x = 15.
Let the other side of the green triangle be marked with z.
Then:
[tex]z\sqrt3=15[/tex] multiply both sides by √3
[tex]3z=15\sqrt3[/tex] divide both sides by 3
[tex]z=5\sqrt3\to y=2(5\sqrt3)=10\sqrt3[/tex]
