QJEEM13Ma9116: JEE Main 2013 Mathematics - Class 12 JEEM13Ma9116 Solution: A B C D is a trapezium such that A B and C D are parallel and B …

Question

Verified Solution • 2025–26 Session moderate

A B C D

is a trapezium such that

A B

and

C D

are parallel and

B C ⊥ C D .

If

∠ A D B = θ, B C = p

and

C D = q,

then AB is equal to:

Accepted Answer

From Sine Rule

\frac{A B}{\sin θ} = \frac{\sqrt{p^{2} + q^{2}}}{\sin (π - (θ + α))}

A B = \frac{\sqrt{p^{2} + q^{2}} \sin θ}{\sin θ \cos α + \cos θ \sin α}

= \frac{(p^{2} + q^{2}) \sin θ}{q \sin θ + p \cos θ}

(As

\cos α = \frac{q}{\sqrt{p^{2} + q^{2}}}

and

\sin α = \frac{p}{\sqrt{p^{2} + q^{2}}}

)

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