JEE PYQ: Properties Of Triangle Question 6
Question 6 - 2019 (10 Jan Shift 2)
With the usual notation, in $\triangle ABC$, if $\angle A + \angle B = 120^\circ$, $a = \sqrt{3} + 1$ and $b = \sqrt{3} - 1$, then the ratio $\angle A : \angle B$, is:
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(1) $7 : 1$
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(2) $5 : 3$
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(3) $9 : 7$
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(4) $3 : 1$
Show Answer
Answer: (1) $7 : 1$
Solution
$C = 60^\circ$. Using Napier’s analogy: $\tan\frac{A-B}{2} = 1 \Rightarrow A - B = 90^\circ$. With $A + B = 120^\circ$: $A = 105^\circ$, $B = 15^\circ$. Ratio $= 7 : 1$.
BETA
