Consider a `DeltaABC` in which the sides are `a = (n +1), b = (n + 2), c = n` with `tan C = 4//3`, then the value of `Delta` is _____

Answer

84

Explanation

`tan C = (4)/(3) rArr cos C = (3)/(5)`
`a = n + 1, b = n + 2, c = n` (given)
`cos C = (a^(2) + b^(2) -c^(2))/(2ab)`
`rArr (3)/(5) ((n +1)^(2) + (n +2)^(2) -n^(2))/(2(n +1) (n +2))`
or `n = 13`
Hence, `a = 14, b = 15, c = 13 and s = 21`
`rArr Delta = (1)/(2) ab sin C`
`= ((1)/(2)) (14) (15) ((4)/(5))`
`= 84`