Which right triangle contains an acute angle where the and of that angle are equal?
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
Which trigonometric function is typically used to find the angle of elevation from a point on the ground to the top of a building when the height of the building and the horizontal distance from the building are known?
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Verified step by step guidance1
Identify the right triangle formed by the building height, the horizontal distance, and the line of sight from the point on the ground to the top of the building.
Recognize that the angle of elevation is the angle between the horizontal distance and the line of sight.
Recall the definitions of the primary trigonometric functions in a right triangle: \(\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}}\).
Since the height of the building corresponds to the side opposite the angle of elevation and the horizontal distance corresponds to the adjacent side, use the tangent function: \(\tan \theta = \frac{h}{d}\).
Therefore, to find the angle of elevation \(\theta\), you would use the inverse tangent function: \(\theta = \tan^{-1} \left( \frac{h}{d} \right)\).
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