Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
What is the length of segment ?
All right triangles that contain the same acute angle are similar. This means that the ratios of corresponding side lengths are equal for all right triangles with the same acute angles. Using the ratios calculated in the previous lesson and properties of similar triangles, we can calculate and estimate unknown side lengths and angles in right triangles.
If we measure the legs of any right triangle with an angle of 25 degrees, the ratio of the leg opposite the 25-degree angle to the leg adjacent to the 25-degree angle will always be 0.466. Therefore, we can find length . Since , we know is 10.7 units.
Similarly, we can estimate the measure of the unknown angles in triangle .
| angle | adjacent leg hypotenuse | opposite leg hypotenuse | opposite leg adjacent leg |
|---|---|---|---|
| 0.643 | 0.766 | 1.192 | |
| 0.500 | 0.866 | 1.732 |
The ratio of the leg opposite angle to the hypotenuse is 0.794. This value is between the value of the ratio of the opposite leg divided by hypotenuse for 50 degrees (0.766) and 60 degrees (0.866). So the measure of angle must be between 50 and 60 degrees. Similarly, the leg opposite angle divided by the leg adjacent to angle gives a ratio of 1.283, which is between the same ratio for 50 degrees (1.192) and 60 degrees (1.732). The exact value turns out to be 52 degrees.