Equilateral triangle and perpendicular line
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 (Itwasntme)
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
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:
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?