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ABC is an isosceles triangle right angle...

ABC is an isosceles triangle right angled at A. forces of magnitude `2sqrt(2),5 and 6` act along BC, CA and AB respectively. The magnitude of their resultant force is

A

4

B

5

C

`11+2sqrt(2)`

D

30

Text Solution

Verified by Experts

The correct Answer is:
B
R `costheta=6cos0^(@)+2sqrt(2)cos(180^(@)-B)+5sin270^(@)`
`Rcostheta=6-2sqrt(2)cosB` . . (i)
`Rsintheta=6sin0^(@)+2sqrt(2)sin(180^(@)-B)+5sin270^(@)`

`Rsintheta=2sqrt(2)sinB-5` . . . (ii)
From Eqs. (i) and (ii), we get
`R^(2)=36+8cos^(2)B-24sqrt(2)cosB+8sin^(2)B+25-20sqrt(2)sinB`
`=61+8(cos^(2)B+sin^(2)B)-24sqrt(2)cosB-20sqrt(2)sinB`
`because` ABC is a right angled isosceles triangle.
i.e., `angleB=angleC=45^(@)`
`thereforeR^(2)=61+8(1)-24sqrt(2)(1)/(sqrt(2))-20sqrt(2)*(1)/(sqrt(2))=25`
`thereforeR=5`.
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