Properties of Triangles 2 Question 1

1. With the usual notation, in ABC, if A+B=120,a=3+1 and b=31, then the ratio A:B, is

(2019 Main, 10 Jan II)

(a) 7:1

(b) 3:1

(c) 9:7

(d) 5:3

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Answer:

Correct Answer: 1. (a)

Solution:

  1. For a ABC, it is given that a=3+1,

b=31 and A+B=120

Clearly, C=60[A+B+C=180]

Now, by tangent law, we have

tanAB2=aba+bcotC2=(3+1)(31)(3+1)+(31)cot602=223cot(30)=13×3=1tanAB2=1=tan45AB2=45AB=90

On solving AB=90 and A+B=120, we get A=105 and B=15

So, A:B=7:1



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