In the diagram, angles \(ABC\) and \(ADE\) are right angles. If \(AC = 35\), \(AE = 11\), and\(BE = 10\) , then what is \(AD\)?

Note that angle A =angle A

And angle CBA = angle EDA

So...by AA congruency....triangle CBA is similar to triangle EDA

[ Since BE = 10 and AE = 11, then BA = 21 ]

So...this implies that

BA / CA = DA / EA

21 / 35 = DA / 11 multiply both sides by 11

11 * 21 / 35 = DA

6.6 = DA