A right triangle has a hypotenuse of length units and one of its acute angles measures . What is the length of each leg of the triangle?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
Given a right triangle with one leg measuring cm, how many distinct right triangles (up to congruence) can be constructed with this information alone?
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Verified step by step guidance1
Understand the problem: We are given a right triangle with one leg measuring 15 cm, and we want to determine how many distinct right triangles (up to congruence) can be formed with this information alone.
Recall that a right triangle is determined by its two legs and the right angle between them. Knowing only one leg length does not fix the other leg or the hypotenuse.
Since the triangle is right-angled, the Pythagorean theorem applies: \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are legs and \(c\) is the hypotenuse. Here, one leg is fixed at 15 cm, but the other leg can vary freely.
Because the other leg can be any positive length, each choice of the second leg length creates a different right triangle (not congruent to others), leading to infinitely many possible triangles.
Therefore, with only one leg length given, there are infinitely many distinct right triangles that can be constructed.
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