In the context of right triangles, what does the trigonometric function (often abbreviated as tg) of an angle represent?
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 , if angle is the right angle, side = and side = , what is the measure of angle ? Round to the nearest degree.
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Verified step by step guidance1
Identify the given elements in the right triangle PQR: angle Q is the right angle (90°), side PQ = 7, and side QR = 8. Since angle Q is right, sides PQ and QR are the legs of the triangle.
Recall that angle R is one of the acute angles, and we want to find its measure. To do this, we can use a trigonometric ratio involving the sides adjacent and opposite to angle R.
Determine which sides are opposite and adjacent to angle R. Side PQ is opposite angle R, and side QR is adjacent to angle R.
Use the tangent function, which relates the opposite side to the adjacent side for an angle in a right triangle: \(\tan(\angle R) = \frac{\text{opposite}}{\text{adjacent}} = \frac{PQ}{QR} = \frac{7}{8}\).
To find angle R, take the inverse tangent (arctangent) of the ratio: \(\angle R = \tan^{-1}\left(\frac{7}{8}\right)\). After calculating this value, round the result to the nearest degree.
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