In ABC, AP ⊥ BC, BQ ⊥ AC B- P-C, A-Q – C then prove that, CPA ~ CQB. If AP = 7, BQ = 8, BC = 12 then find AC.

Consider CPA and CQB,
CPA CQB [ From figure, angle is equal to 90˚]
PCA QCB [ Common angle]
CPA ~ CQB, [AA test of similarity]
Hence proved.
AC/BC = AP/BQ [ corresponding sides of similar triangles]
Given AP = 7, BQ = 8, BC = 12
AC/12 = 7/8
AC = 12×7/8
AC = 10.5
Hence measure of AC is 10.5 units.