Final answer:
The question asks for the method to find the equation of a line using similar right triangles. To solve such a problem, the slope must be determined using trigonometric ratios and a point on the line to find the y-intercept for the slope-intercept form of the line equation.
Step-by-step explanation:
The question involves finding the equation of the line in similar right triangles ABD and ACE. We are given different side measurements and asked to determine the correct approach to finding the line's equation.
To find the equation of a line using right triangles, you typically need to use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. When dealing with right triangles, the slope can often be found by using the trigonometric ratios of the angles present, which are defined as the sine, cosine, and tangent of the angle and relate the lengths of the legs to the hypotenuse (from Figure 5.17).
None of the options A to D provides a complete method to solve for the line equation, as they each contain pieces of unrelated information. The proper method would involve determining the slope from the similar triangles and then using a point on the line to solve for b, the y-intercept, to write the final equation.