Assume that alpha is an angle in standard position whose terminal side contains the given point and that 0 < alpha < pi/2. Find the radian measure of alpha to the nearest 10th, (square root 5, 1)
We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the point (sqrt(5), 1) and the x-axis.
The hypotenuse is the line segment connecting the origin (0,0) to the given point, and its length is sqrt((sqrt(5))^2 + 1^2) = sqrt(5+1) = sqrt(6).
Since 0 < alpha < pi/2, alpha is an acute angle in the first quadrant.
In the right triangle, the angle alpha is the angle whose adjacent side is sqrt(5) and whose hypotenuse is sqrt(6).
We can use the cosine function to find the measure of alpha.
cos(alpha) = adjacent/hypotenuse = sqrt(5)/sqrt(6)
To find alpha, we can take the inverse cosine (also known as arccosine) of sqrt(5)/sqrt(6).
alpha = arccos(sqrt(5)/sqrt(6)) ≈ 0.590 rad
Therefore, the radian measure of alpha to the nearest tenth is approximately 0.6.