Problem Solving

Tough problem,

its a semi circle angle O is 90 degrees, determine the value of "s" on point B?

options
0.5
1
2^0.5
3^.33
1/(2)^.5

We can make a right triangle using points A and 0 and the x-axis, which gives us legs of sqrt(3) and 1. We know that this must be a 30-60-90 triangle. Angle A is opposite the sqrt(3) side, so it must be 60 degrees. The angle at point 0 is opposite the side of 1, so it must be 30 degrees. The angle formed at the x-axis must be 90 degrees, and to fit the side ratio, the hypotenuse, which is the segment AO, must be 2.

We also know that a half-circle has 180 degrees. We know that 0 is 90, and we determined that the angle in our right triangle at point 0 is 30 degrees. This leaves 60 degrees for the angle formed by segment BO and the x-axis. We can again create a 30-60-90 triangle, and from there, we can see that s must be 1 and t must be sqrt(3).

Bill, how do you know it is a 30 60 90 right angle triangle? Why couldn't it be a 45 45 90 right angled triangle?