The triangles shown in adjoining figures are similar. Find the values of a and b.

Explanation

` angleA=angleR, angleB=angleP and angleC= angleQ`
`triangleABC~ triangleRPQ`
( AAA similarity)
`undersetunderset("first two")(darr)((AB)/(RP))=undersetunderset("Last two")(darr)((BC)/(PQ))=undersetunderset("First and last")(darr)((AC)/(RQ))`
(corresponding sides of similar triangles are proportional )
`a/8 = (7.5)/6= 4/b`
`a/8 = (7.5)/6 and 4/b = (7.5)/6`
`a= (8xx7.5) /6 and b= ( 4xx6)/(7.5)`
a= 1-0 and b= 3.2