We are given the measures of the angles in a pair of similar triangles. We also know the side lengths. We want to find the value of x. Let's make a picture of this triangles and mark the known values on it.
Let's begin by recalling that in similar triangles corresponding sides are proportional. With this information, we can create a proportion by writing the ratios of the lengths of a corresponding sides.
Ratio of Corresponding Sides
3/x-0.46
3.25/x
4.23/x+1.81
To find the value of x, we will use only two of the above ratios. Let's write a proportion using the first and the second ratio.
3/x-0.46 = 3.25/x
Now, we will solve the equation for x. To do this we will use a cross multiplication. When using cross multiplication, we treat x-0.46 like a single term.
