Hey. Let me help you on this one.
If we take a look at these triangles, we will notice that they are created by intersecting lines. I will be attaching an image alongside this answer to help you identify them.
Since vertical angles are congruent, all we need to do is set up a ratio. We can find out how big right triangle is compared to the left triangle if we find a side that's known for both figures.
One side known for both figures is the base (5 in, and 15 in). Left angle's side is three times smaller than right angle's side.
[tex] \frac{15}{x} =5[/tex]
[tex]x=3[/tex]
Now, that we know the size ratio between two shapes, we can use it to determine size of side [tex]x[/tex].
As you can see, the same side is known on a smaller triangle - 8 inches. We know that left triangle is three times smaller, so we will need to make 8 inches three times bigger than it is to fulfill the size requirement.
[tex]8*3=24[/tex]
Answer: Length of the unknown side is 24 inches.
