Question

1. Find the value of x and y



2. Find the value of x and y

explain

Answer 1

`\large\boxed{1.\ x=10,\ y=10\sqrt3}\\\boxed{2.\ x=15,\ y=10\sqrt3}`

Explanation:

Look at the pictures.

1.

We have the triangle 30° - 60° - 90°. The sides are in proportion 1 : √3 : 2.

Therefore:

`x=(20)/(2)=10,\ y=10\sqrt3`

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:

`x=(30)/(2)=15`

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:

`z\sqrt3=15` multiply both sides by √3

`3z=15\sqrt3` divide both sides by 3

`z=5\sqrt3\to y=2(5\sqrt3)=10\sqrt3`