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A particular case of Caccetta-H\"{a}ggkvist conjecture, says that a digraphof order $n$ with minimum out-degree at least $1/3n$ contains a directed cycleof length at most 3. Recently, Kral, Hladky and Norine proved that a digraph oforder $n$ with minimum out-degree at least $0.3465n$ contains a directed cycleof length at most 3 (which currently is the best result). A weaker particularcase says that a digraph of order $n$ with minimum semi-degree at least $1/3n$contains a directed triangle. In a recent paper, by using the result of Kral etal, the author proved that for $\beta\geq 0.343545$, any digraph $D$ of order$n$ with minimum semi-degree at least $\beta n$ contains a directed cycle oflength at most 3 (which currently is the best result). This means that for agiven integer $d\geq 1$, every digraph with minimum semi-degree $d$ and oforder $md$ with $m\leq 2.91082$, contains a directed cycle of length at most 3.In particular, every oriented graph with minimum semi-degree $d$ and of order$md$ with $m\leq 2.91082$, contains a directed triangle. In this paper, byusing the result of Kral et al, we prove that every oriented graph with minimumsemi-degree $d$, of order $md$ with $2.91082< m\leq 3$ and of strongconnectivity at most $0.679d$, contains a directed triangle. This will beimplied by a more general and more precise result, valid not only for $2.91082<m\leq 3$ but also for larger values of $m$. As application, we improve twoexisting results. The first result (Authors Broersma and Li), concerns thenumber of the directed cycles of length 4 of a triangle free oriented graph oforder $n$ and of minimum semi-degree at least $\frac{n}{3}$. The second result(Authors Kelly, K\"{u}hn and Osthus), concerns the diameter of a triangle freeoriented graph of order $n$ and of minimum semi-degree at least $\frac{n}{5}$.

Strong connectivity and directed triangles in oriented graphs. Partial results on a particular case of the Caccetta-H\"aggkvist conjecture