What is the length of the chord of a unit circle which subtends an angle 2\theta at the centre, where \theta \lt 45^\circ?
- A. \sin 2\theta
- B. \cos 2\theta
- C. 2 \sin \theta ✓
- D. 2\cos\theta
Correct Answer: C. 2 \sin \theta
Explanation
Drawing a perpendicular from the center to the chord bisects the angle 2\theta into two angles of \theta, and bisects the chord. The half-length of the chord in the resulting right triangle is r \sin \theta. With r=1, the full length of the chord is 2 \sin \theta.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...