Since box-shadow
won't work, you have to apply a drop shadow filter on the triangle:
.triangle {
width: 0;
height: 0;
border-style: solid;
border-width: 200px 200px 0 0;
border-color: #007bff transparent transparent transparent;
-webkit-filter: drop-shadow(1px 1px 1px rgba(0,0,0,.5));
filter: drop-shadow(1px 1px 1px rgba(0,0,0,.5));
}
<div class="triangle"></div>
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