JSFiddle - React, Tailwind, and code Playground

HTML

<div class='user-nav'>
    <button class="drop-menu-button">Menu</button>
</div>
<div class='drop-menu'>
    <ul>
        <li><a href='#'>My Profile</a>
        <li><a href='#'>Logout</a>
    </ul>
</div>

CSS

.user-nav {
    height: 50px;
    background-color: black;
}

.drop-menu {
    position: relative;
    background-color: red;
}
.drop-menu ul{
    display: none;
}

.drop-menu.visible::before {
  content: '';
  position: absolute;
  width: 0;
  height: 0;
  left: 30px;
  top: -20px;
  border: 10px solid;
  border-color: transparent transparent red transparent;
  display:block;
}

JavaScript

$('.drop-menu-button').click(function() {
    $('.drop-menu').addClass('visible');
    $('.drop-menu ul').slideToggle('',function(){
        if(!$(this).is(':visible')){
            $('.drop-menu').removeClass('visible');
        }
    });
});