# In a triangle, length of 2 larger sides is 24 & 22 resp.. if angle r in AP, then 3rd side is.........................Also give reason behind choice of sides...........

Chetan Mandayam Nayakar
312 Points
13 years ago

Dear Piyush,

the angle opposite 22 is 60 degrees. Let third side be x,

from cosine law, 222=x2+242 -2*24*x*cos(60)

x2-24x+92=0

x=12±√52=12±2√13

All the best.

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Chetan Mandayam Nayakar – IIT Madras

509 Points
13 years ago

let ABC be the triangle...

angles are in ap so 2B=A+C...........1

A+C=90-B..........2

from 1 and 2

B=60 and so A and C can be 30 and 90

now draw a triangle ABC right angled at C

AB is the hypotenuse therefore AB=24

let the other sides be 22 and x

now 24^2 =22^2 +x^2

X=+-2sqrt23

Surya Anuraag Duvvuri
39 Points
13 years ago

te angle opposite to 22 is 60 degrees,let the third side be a

now from cos rule 22^2=x^2+24^2-2*x*24 Cos60

x^2-24x+92=0

x = 12+-rt52=12+-2rt13