In a right triangle, if point A is at and point B is at , what is the vertical change from point A to point B?
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
Given a right triangle with an angle , in which triangle is the value of equal to ?
A
A triangle where the side opposite angle is units and the hypotenuse is units.
B
A triangle where the hypotenuse is units and the side adjacent to angle is units.
C
A triangle where the side opposite angle is units and the side adjacent to angle is units.
D
A triangle where the side opposite angle is units and the side adjacent to angle is units.
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Verified step by step guidance1
Recall the definition of the tangent function in a right triangle: \(\tan(x) = \frac{\text{opposite}}{\text{adjacent}}\).
Given that \(x = \tan^{-1}\left(\frac{3.1}{5.2}\right)\), this means the ratio of the side opposite angle \(x\) to the side adjacent to angle \(x\) is \(\frac{3.1}{5.2}\).
Identify which sides correspond to the opposite and adjacent sides relative to angle \(x\) in the triangle options provided.
Check each triangle option to see if the ratio \(\frac{\text{opposite}}{\text{adjacent}}\) equals \(\frac{3.1}{5.2}\).
Select the triangle where the side opposite angle \(x\) is 3.1 units and the side adjacent to angle \(x\) is 5.2 units, as this matches the given tangent inverse expression.
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