Given two similar right triangles, one with sides , , and , and the other with sides , , and , 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
Solving Right Triangles
Multiple Choice
In a right triangle , if the length of is units and angle is , what is the length of side opposite angle ?
A
units
B
units
C
units
D
units
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Verified step by step guidance1
Identify the right triangle FGH and note that angle G is 30° and side FH (the hypotenuse) is 18 units.
Recall that in a right triangle, the side opposite a 30° angle is half the length of the hypotenuse.
Use the formula for the side opposite the 30° angle: \(\text{opposite} = \frac{1}{2} \times \text{hypotenuse}\).
Substitute the given hypotenuse length into the formula: \(\text{opposite} = \frac{1}{2} \times 18\).
Calculate the length of side FG, which is opposite angle H, by simplifying the expression (do not provide the final numeric answer here).
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