I didn't quite know what to put as title, so I'm sorry if the title doesn't give a clue of what is to be found
Well, here's the question:
Qu: The points S and T are located on the respective sides PQ and PR of an equilateral triangle PQR so that ST = TR and ST is perpendicular to PQ. Given that the length of QR is 1, the length of ST is
A.
B.
C.
D.
E.
I proceeded with finding the angles, angle STR being 150 degrees and angle TSR = angle TRS = 15 degrees.
Then, I found the length of QS, since QRS is a right angle with one of the angles being 45 degrees. QS = = SR.
Then, fron the sine rule, I know that:
So,
Now, I don't know the exact form on sin(15) and I don't see any square root of 2 in any of the choices. Is there a quicker/simpler way to solve this?
Thanks!
So, triangle SQT is a 30-60-90 triangle, and if we label the hypotenuse QT as having length y and TR as having length x, we get cos(pi/6) = sqrt(3)/2 = x/y which gives y = 2x/sqrt(3). So x+2x/sqrt(3) = 1. After some algebraic manipulation I get answer C.