I know my question doesn’t make too much sense, but it is tricky to explain in a sentence. Basically, I am given a right triangle, and I am given three lengths; one of a leg (19.6), one as a distance from the right angle to a second vertical line (20.8), that is also parallel to the known leg, and one as a length of that line (6.2). This line serves to make a second, similar, right triangle. How would I find the length of the second leg of that smaller right triangle? (P.S., this is a practice question, and the answer is apparently supposed to be 15.0, but the answers on these practice sheets aren’t always right)
EDIT: Here is a link to the diagram of the question (not to scale):
I would have to disagree with the solution of 15. (I am basing my answer off of the diagram as the question was hard to interpret under the assumption that the diagram is accurate.)
The insight needed to solve this question is to realize that the two parallel lines make two similar triangles. Because both the leg in question and the hypotenuse can be considered transversals that intersect two parallel lines, we know they have equal corresponding angles. We know their corresponding angles the angle between x and 6.2 is a right angle because the other angle is a right angle. Also, the angle between the leg with length 19.2 and the hypotenuse is equal to the angle between the leg with length 6.2 and the hypotenuse. We know now that these are similar triangles as they have the same angles and we can thus conclude that the ratio of their side lengths must be equal.
$$\frac{x}{6.2} = \frac{20.8+x}{19.6}$$ $$19.6x=(20.8+x)*6.2$$ $$13.4x=128.96$$ $$x=\frac{128.96}{13.4} \approx 9.62$$
Hope this makes sense!