Question 9 of 10 On a unit circle, the terminal point of θ is
(√3/2,1/2)
What is θ?
A. π/2 radians
B. π/6 radians
C. π/4 radians
D. π/3 radians

30° or π/6 rad

Step-by-step explanation:

Imagine or draw a right triangle with horizontal side (√3)/2 and vertical side 1/2.  Verify that the hypotenuse of this triangle is 1 (which it must be, since the circle is a unit circle):  [(√3)/2)^2 + (1/2)^2 = r^2, which leads to r = 1.  

The tangent function tan x = opp/adj takes on the following values here:

tan x = 1/2 over √(3/2)/2, or 1/√3.  Using a calculator or a table of trig function values, we find that the angle x is π/6 radians, or 30°

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the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.