Which of the following statements is true about the tangent function in a right triangle?
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
Triangle xyz is isosceles. Angle y measures degrees. What expression represents the measure of angle x?
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Verified step by step guidance1
Recall that in any triangle, the sum of the interior angles is always \(180^\circ\). So, we have the equation: \(x + y + z = 180\).
Since triangle XYZ is isosceles, two of its angles are equal. Identify which angles are equal. Given that angle \(y\) measures \(a\) degrees, the other two angles, \(x\) and \(z\), must be equal.
Set \(x = z\) because the triangle is isosceles and these two angles are the ones opposite the equal sides.
Substitute \(z\) with \(x\) and \(y\) with \(a\) in the angle sum equation: \(x + a + x = 180\).
Combine like terms to get \$2x + a = 180\(, then solve for \)x$ by isolating it: \(x = \frac{180 - a}{2}\).
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