JSFiddle - React, Tailwind, and code Playground

HTML

<div class="table container">
    <div class="table-row header">
        <div>This is the header whose height is unknown</div>
        <div>This is the header whose height is unknown</div>
        <div>This is the header whose height is unknown</div>
    </div>
    <div class="table-row body">
        <div class="table-cell body-content-outer-wrapper">
            <div class="body-content-inner-wrapper">
                <div class="body-content">
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is unknown</div>
                    <div>This is the scrollable content whose height is...

CSS

.table {
    display: table;
}

.table-row {
    display: table-row;
}

.table-cell {
    display: table-cell;
}

.container {
    width: 400px;
    height: 300px;
}

.header {
    background: cyan;
}

.body {
    background: yellow;
    height: 100%;
}

.body-content-outer-wrapper {
    height: 100%;
}

.body-content-inner-wrapper {
    height: 100%;
    position: relative;
    overflow: auto;
}

.body-content {
    position: absolute;
    top: 0;
    bottom: 0;
    left: 0;
    right: 0;
}