Let n `in` Z and `DeltaABC` be a right tirangle with angle at C . If sin A and sin B are the roots of the equadratic equation `(5n + 8) x^(2) - (7n - 20) x + 120 = 0` , then find the value of n.

Explanation

We have `sin A + sin B = (7n - 20)/(5n + 8)` …(1)
`siin A .sin B = (120)/(5n + 8)` …(2)
Also, ` sin^(2) A + sin^(2) B = 1` ( as `angle C = 90^(@))`
`therefore ( sin A + sin B )^(2) - 2 sin A sin B = 1`
`rArr n^(2) - 65n - 66 = 0`
`rArr (n - 66) ( n+ 1) = 0`
`therefore n - 66`