Trigonometric Equations Question 379
Question: The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is $ 60^{o} $ . If the third side is 3, the remaining fourth side is
[MNR 1994]
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: A
Solution:
Let the fourth side be of ?d? length. We know that $ AB^{2}+BC^{2}-2AB.BC\cos 60^{o}=AC^{2} $ $ =CD^{2}+DA^{2}-2CD.DA\cos 120^{o} $ (by cosine rule) or $ 4+25-2.,2.,5.\frac{1}{2}=9+d^{2}-3d $ Þ $ d^{2}+3d-10=0\Rightarrow d=-5 $ or $ d=2 $ ; \ $ d=2 $ .
BETA
