Question

There are two similar triangles in the diagram. Find the unknown measurement.

Answer 1

The unknown measurement in the diagram is \(x = 8\) units.

Step-by-step explanation:

In the given diagram, we have two similar triangles, △ABC and △DEF. According to the properties of similar triangles, corresponding angles are equal, and corresponding sides are in proportion. Let's denote the length of side AB as a, BC as b, DE as c, and EF as d.

Now, considering the ratios of corresponding sides, we have:

`\[^AC / ^DF = ^BC / ^EF\]`

Since the triangles are similar:

`\[^a / ^c = ^b / ^d\]`

Now, substitute the known values:

8 / x = 12 / 15

To find x, cross-multiply and solve for x:

8×15 = 12x

120 = 12x

x = 10

However, we need to remember that the question asked for the length of DE, not DC. Since DC is the sum of DE and EC, and EC is given as 2 units, we subtract it from x to find DE:

`\[DE = x - EC = 10 - 2 = 8\]`

Therefore, the unknown measurement, x, is 8 units.

Answer 2

To find unknown measurements in similar triangles, you can use trigonometry and proportions. The scale factors and scale measurements provided in a question allow you to set up and solve proportions to find the actual dimensions or distances.

Step-by-step explanation:

The student's question involves finding unknown measurements in similar triangles using trigonometry and proportions. The concept of similar triangles is used in trigonometry to relate various lengths and angles within geometric figures and can also be employed in practical scenarios such as triangulation to calculate distances.

When dealing with scale factors and scale drawings or models, setting proportions allows you to find unknown lengths by comparing the scale length to the actual length.

For example, if the scale factor is 2 inches to 3 feet and the scale measurement is 6 inches, the proportion is: (2 inches/3 feet) = (6 inches/actual feet). Solving this proportion will give the actual dimension. Another application of proportions is when you are given a length ratio, such as 1 inch to 2000 miles, and the scale length; you create a proportion like (1 inch/2000 miles) = (3 inches/x miles) to find the unknown distance x.

The complete question is: There are two similar triangles in the diagram. Find the unknown measurement.is: