In a right triangle, one of the acute angles measures . What is the measure of the other acute angle?
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
Solving Right Triangles
Multiple Choice
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?
A
The legs have lengths units and units.
B
The legs have lengths units and units.
C
The legs have lengths units and units.
D
The legs have lengths units and units.
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Verified step by step guidance1
Identify the given information: the hypotenuse length is 10 units, and one acute angle is 30° in a right triangle.
Recall the properties of a 30°-60°-90° right triangle: the sides are in the ratio 1 : \(\sqrt{3}\) : 2, where the hypotenuse corresponds to 2.
Set up the proportion using the hypotenuse: if the hypotenuse is 10 units, then the side opposite 30° (the shorter leg) is half the hypotenuse, so calculate it as \(\frac{10}{2}\).
Calculate the length of the other leg (opposite 60°) using the ratio: multiply the shorter leg by \(\sqrt{3}\) to find the longer leg.
Express the lengths of the legs as \$5$ units and \(5\sqrt{3}\) units, corresponding to the sides opposite 30° and 60°, respectively.
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