Triangles ABC and DEF are similar with corresponding sides in proportion. Solving the ratio (30/24) = (40/x) yields x = 32. Thus, the length of DF is 32 units.
To solve this problem, we can use the properties of similar triangles. Triangles ABC and DEF are similar since they both have a 90-degree angle and an angle of 35 degrees.
The corresponding sides of similar triangles are proportional. Let's denote the length of DF as x. Then, we can set up a proportion using the corresponding sides:
(AB / DE) = (AC / DF)
Substitute the given values:
(30 / 24) = (40 / x)
Now, cross-multiply to solve for x:
30 * x = 24 * 40
30x = 960
x = 960 / 30
x = 32
Therefore, the length of DF is 32 units.
Complete question:
In ΔABC, m∠A = 90º and m∠B = 35º. In ΔDEF, m∠E = 35º and m∠F = 55º. If AB=30, AC=40, and DE=24, what is the length of DF?