Algebra Two and Geometry Help please?

Question

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Answer 1

the squareroot of two,

since you have a 30-60-90 right triangle, and the length of the sides is in the proportion 30--> x
60--> x times the squareroot of 3, and 90--> 2x, in this case, x is the squareroot of 2, so the whole side of ST is 2times the squareroot of 2, but the one triangle is equilateral, since two of the angles are 60 degrees, the third must be since the sum of the three angles are 180 degrees. this means all the sides are the same in length, the squareroot of 2. so subtract the squareroot of 2 from 2 times the squareroot of two, and you get the squareroot of 2

Answer 2

PT = 2sqrt(2)
PS = PR = sqrt(2)
ST = PT - PS = 2sqrt(2) - sqrt(2) = sqrt(2)