Given a right triangle where angle is one of the non-right angles, the side opposite has length , the side adjacent to has length , and the hypotenuse has length , what is the 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 that and , what is ?
A
B
C
D
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Verified step by step guidance1
Identify the points and angles involved: We have points B, G, C, and F, and the angles \( m\angle BGC = 6x - 13 \) degrees and \( m\angle CGF = 4x + 3 \) degrees. We want to find \( m\angle BGF \).
Recognize that points B, G, C, and F are arranged such that \( \angle BGC \), \( \angle CGF \), and \( \angle BGF \) are angles around point G. The sum of these three angles around point G is 180 degrees if they lie on a straight line or 360 degrees if they form a full circle. Here, since \( B, G, C, F \) are points on a plane and the problem suggests these three angles are adjacent, we consider the straight angle case where the sum is 180 degrees.
Set up the equation expressing that the sum of the three angles around point G is 180 degrees:
\( m\angle BGC + m\angle CGF + m\angle BGF = 180^\circ \)
Substitute the given expressions for \( m\angle BGC \) and \( m\angle CGF \) into the equation:
\( (6x - 13) + (4x + 3) + m\angle BGF = 180^\circ \)
Solve for \( m\angle BGF \) by isolating it on one side:
\( m\angle BGF = 180^\circ - (6x - 13) - (4x + 3) \)
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