In an isosceles triangle, the angles opposite the equal sides are equal, so Angle P = Angle R.

If the ratio is 2:1, then the sides of triangle STU will be 3*2, 4*2, and 5*2, which are 6, 8, and 10.

Since AB = AC, angles B and C are equal. Therefore, angle B + angle C = 140 degrees, and each angle is 70 degrees.

Using the sine rule: a/sin(A) = b/sin(B) => a = b * sin(A)/sin(B) = 10 * sin(30)/sin(60) = 10 * 0.5/(√3/2) = 5.

Triangle XYZ is a right triangle because 8^2 + 6^2 = 10^2.