Given a right triangle where side is units, side is units, and is the hypotenuse, what is the measure of angle ? Round to the nearest whole degree.
Table of contents
- 0. Review of College Algebra4h 45m
- 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
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
Given a right triangle where one of the acute angles is and the hypotenuse is , what is the length of the side opposite the angle (let this length be )?
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Verified step by step guidance1
Identify the given information: a right triangle with one acute angle measuring 30° and the hypotenuse length of 10.
Recall the special property of a 30°-60°-90° right triangle: the side opposite the 30° angle is exactly half the length of the hypotenuse.
Set the length of the side opposite the 30° angle as \(x\) and write the relationship using the property: \(x = \frac{1}{2} \times \text{hypotenuse}\).
Substitute the given hypotenuse length into the equation: \(x = \frac{1}{2} \times 10\).
Simplify the expression to find the length of the side opposite the 30° angle (do not calculate the final value here, just set up the expression).
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