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! :)