If is an angle such that , what is the approximate value of ?
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, what is the value of ?
A
B
C
D
0 Comments
Verified step by step guidance1
Recall that the tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Mathematically, this is expressed as \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).
Identify the angle given in the problem, which is \(60^\circ\), and consider a right triangle where one of the angles is \(60^\circ\).
Use the properties of a 30-60-90 right triangle, where the sides are in the ratio \(1 : \sqrt{3} : 2\), with the side opposite \(30^\circ\) being 1, opposite \(60^\circ\) being \(\sqrt{3}\), and the hypotenuse being 2.
Apply the tangent definition for the \(60^\circ\) angle: \(\tan(60^\circ) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{\sqrt{3}}{1}\).
Conclude that \(\tan(60^\circ) = \sqrt{3}\), which matches the known exact value for the tangent of \(60^\circ\).
Related Videos
Related Practice
Multiple Choice

