wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If in ABC, (b+c)11=(c+a)12=(a+b)13, then cosA is equal to:


A

15

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

57

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

1935

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

15


Explanation for the correct option:

Step 1: Find the value of a+b+c.

Let (b+c)11=(c+a)12=(a+b)13=k

b+c=11k...1c+a=12k...2a+b=13k...3

By adding 1,2,and3, we get

b+c+c+a+a+b=11k+12k+13k2a+b+c=36ka+b+c=18k

Step 2: Find the value of a,b,andc.

a+b+c=18k13k+c=18kc=5k

Similarly

a+b+c=18ka+11k=18ka=7k

and

a+c+b=18k12k+b=18kb=6k

Step 3: Apply cosine rule.

As per Cosine Rule,

2bccosA=b2+c2-a2cosA=b2+c2-a22bc=36k2+25k2-49k22×30k2=12k260k2=15

Hence, option A is correct.


flag
Suggest Corrections
thumbs-up
8
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Division of Fractions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon