A line in the coordinate plane has an angle of elevation of 53 degrees. Find the slope of the line correct to four decimal places.

Let's make a reference triangle with the x and y axes as the legs of the right triangle. The hypotenuse is the slope where the angle of elevation is based. Given an angle of elevation of 53 degrees, the remaining angle is 37 degrees. Use sine law to calculate for the hypotenuse:

(sin 53/x) = (sin 37/y) = (sin 90/z)

solve for x, y and z. The slope is y/x