ABCD is a trapezium such that AB and CD are parallel and [BC CD.] If [ ADB = ,,BC = p] and…

Question

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $$BC \bot CD.$$ If $$\angle ADB = \theta ,\,BC = p$$ and $CD = q,$ then AB is equal to:

Accepted Answer

From Sine Rule

$${{AB} \over {\sin \theta }} = {{\sqrt {{p^2} + {q^2}} } \over {\sin \left( {\pi  - \left( {\theta  + \alpha } \right)} \right)}}$$

$$AB = {{\sqrt {{p^2} + {q^2}} \sin \theta } \over {\sin \theta \cos \alpha  + \cos \theta \sin \alpha }}$$

$$ = {{\left( {{p^2} + {q^2}} \right)\sin \theta } \over {q\sin \theta  + p\cos \theta }}$$

(As $$\cos \alpha  = {q \over {\sqrt {{p^2} + {q^2}} }}$$ and $$\sin \alpha  = {p \over {\sqrt {{p^2} + {q^2}} }}$$ )

Solutions · 1