Unit 4, Lesson 5
Working with Ratios in Right Triangles
Geometry
5.3
Activity
How Long?
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What is the length of segment
? - In a right triangle with one angle measuring 40 degrees, the leg opposite the 40-degree angle is 5 cm. What is the length of the hypotenuse?
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What is the length of segment
? - In a right triangle with one angle measuring 70 degrees, the leg opposite the 70-degree angle is 12 cm. What is the length of the leg adjacent to the 70-degree angle?
Student Lesson Summary
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
Similarly, we can estimate the measure of the unknown angles in triangle
| angle | adjacent leg |
opposite leg |
opposite leg |
|---|---|---|---|
| 0.643 | 0.766 | 1.192 | |
| 0.500 | 0.866 | 1.732 |
The ratio of the leg opposite angle
None
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