In parallelogram LMNO, if angle L measures , what is the measure of angle O?
Table of contents
- 0. Review of College Algebra4h 45m
- 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
2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
In right triangle PQR, angle P is , angle Q is , and the length of side PQ is units. What is the length of side QR?
A
units
B
units
C
units
D
units
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Verified step by step guidance1
Identify the given information: In right triangle PQR, angle P = 30°, angle Q = 60°, and side PQ = 8 units. Since the triangle is right-angled, the remaining angle R must be 90°.
Determine the position of the sides relative to the angles: Side PQ is opposite angle R (90°), so PQ is the hypotenuse of the right triangle.
Recall the properties of a 30°-60°-90° triangle: The sides are in the ratio 1 : \(\sqrt{3}\) : 2, where the side opposite 30° is the shortest, opposite 60° is \(\sqrt{3}\) times the shortest, and the hypotenuse is twice the shortest side.
Use the side ratio to find the length of side QR, which is opposite angle P (30°). Since PQ is the hypotenuse and equals 8 units, the shortest side (opposite 30°) is half of the hypotenuse: \( \frac{8}{2} = 4 \) units.
Calculate side QR, which is opposite angle Q (60°), by multiplying the shortest side by \(\sqrt{3}\): \( 4 \times \sqrt{3} \). This gives the length of side QR.
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