How would one solve similar right triangles if the first triangle has y and x as legs and a (altitude) as hypotenuse, and the second triangle has one leg of 50, the other is a, and the hypotenuse is 100. I solved for a, and it came out to be 86.6? Is this correct? How do I solve x and y?

Answer 1

your value of a is correct.
Actually your given triangle is a 30-60-90 right-angled triangle with sides in the ratio
1 : √3 : 2
= 50: 50√3:100

You didn't say which of the legs is the x and the other the y.

Assume the x is opposite the 30° angle
then the sides would be
x : √3 x : 2x , so that y = √3 x , h = 2x

make the necessary changes if y is the side opposite the 30° angle