23. A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord? (a) √√2-1 units (b) √3-1 units (c) √2 units (d) √√3 units 24. What is (1+cote cosece) (1 + tan 0 + sec 0) equal to? (a) 1 (b) 2 (c) 3 (d) 4
Answers
Answer: The length of Cord = √3 units.
Step-by-step explanation:.
Please see the attached document for step by step explanation.
Length of chord is √3 units if A chord subtends an angle 120° at the centre of a unit circle.
Given:
- A chord subtends an angle 120° at the centre of a unit circle
To Find:
- Length of the chord
Solution:
Unit circle has radius 1 unit
Assume that chord AB subtend an angle 120° at the centre O .
ΔAOB with OA = OB = 1 unit ( radius of circle)
∠AOB = 120°
Using cosine low of triangle ΔABC with sides a , b and c
c² = a² + b² - 2abcosC
AB² = OA² + OB² - 2(OA)(OB) cos ∠AOB
Substituting the Values:
AB² = 1² + 1² - 2(1)(1)cos 120°
=> AB² = 1 + 1 - 2 (-1/2)
=> AB² = 2 + 1
=> AB² = 3
=> AB = √3 units
Length of chord is √3 units
correct option is d)
2nd part of Question is not clear,
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