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In triangle ABC, we are given that 3 sin...

In triangle ABC, we are given that `3 sin A +4 cos B=6` and `4 sin B+3 cos A=1`. Then the measure of the angle C is -

A

`30^(@)`

B

`150^(@)`

C

`60^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
Square & add both equations
`9+16+24 sin (A+B)=37`
`sin (A+B)=1/2 rArr A+B=pi/6 rArr C=(5pi)/6` (wrong)
`rArr A+B=(5pi)/6 rArr C=pi/6`
because `C=(5pi)/6`
does not follow equation `3 sin A + 4 cos B =6`
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