Find the missing side lengths. leave your answers as radicals in simplest form

Hey there!!

If we look at the diagram closely, we will see that the triangle is a right angled triangle.

We figured out two angles, 60 and 90.

As the total sum of the angles in a triangle is 180, the missing angle would be ...

... 180 - ( 90 + 60 )

... 180 - 150

... 30

Hence, the angles of the triangle are - 30 , 60 and 90.

We could also apply the Pythagorean theorem to find the sides.

If we have a 30-60-90 triangle, the hypotenuse is 2x. The height is x and the base is √3x

Now, looking at the triangle, we know that the hypotenuse is 'x', base is 'y' and height is (15√2)/2

Hence, the base would be √3(height)

... √3(15√2)/2

... (15√6)/2

The hypotenuse = 2 ( 15√2/2)

... 15√2

Hence, the sides =

Hypotenuse - 15√2

Height = (15√2) / 2

Base = (15√6) / 2

Hope my answer helps!

Happy thanksgiving! :)