Trigger menu open from a button

I have a menu defined in my html:

 <md-menu>
 <!-- Trigger element is a md-button with an icon -->
    <md-button ng-click="$mdOpenMenu($event)" class="md-icon-button" aria-label="Open sample menu">
        <md-icon md-svg-icon="call:phone"></md-icon>
       </md-button>
    <md-menu-content>
        <md-menu-item><md-button ng-click="doSomething()">Do Something</md-button></md-menu-item>
    </md-menu-content>
</md-menu>

and a button somewhere else on the same html:

<md-button ng-click="openOtherMenu()">Open Menu</md-button>

I want that clicking on the Open Menu button will trigger the opening of the menu. I am not sure what needs to be in openOtherMenu(). Any ideas?