Question

For the points C(0,2) and D(5,9), calculate the angle between CD and y axis

Answer 1

first off, let's find the length of CD, bearing in mind that point C is sitting right on the y-axis.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad D(\stackrel{x_2}{5}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(5-0)^2+(9-2)^2}\implies CD=\sqrt{5^2+7^2}\implies CD=\sqrt{74}$

Check the picture below.

make sure your calculator is in Degree mode.