Given a right triangle with an angle of and an adjacent side of length , which equation can be used to solve for the length of the side opposite the angle?
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
Trigonometric Functions on Right Triangles
Multiple Choice
In right triangle , angle is the right angle, side is units, and side is units. What is the measure of angle ? Round to the nearest whole degree.
A
degrees
B
degrees
C
degrees
D
degrees
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Verified step by step guidance1
Identify the sides of the right triangle relative to the angle you want to find. Here, angle \( \angle BAC \) is the angle at vertex A. The side opposite to this angle is \( BC = 6 \) units, and the hypotenuse is \( AB = 10 \) units.
Recall the trigonometric ratio that relates the opposite side and the hypotenuse: the sine function. It is defined as \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
Set up the equation using the sine function for angle \( \angle BAC \): \( \sin(\angle BAC) = \frac{BC}{AB} = \frac{6}{10} \).
To find the measure of \( \angle BAC \), take the inverse sine (arcsin) of \( \frac{6}{10} \): \( \angle BAC = \sin^{-1}\left(\frac{6}{10}\right) \).
Use a calculator to evaluate the inverse sine and then round the result to the nearest whole degree to get the measure of \( \angle BAC \).
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