The height of a certain mountain in California is \( 14,658 \mathrm{ft} \). The depth of a known trench in the Pacific Ocean is \( -23,792 \mathrm{ft} \). What is the difference between the height of the mountain and the depth of the trench? What is the difference between the height of the mountain and the depth of the trench? ft

To find the difference between the height of the mountain and the depth of the trench, you can think of both values on a number line. The height of the mountain is \( 14,658 \) ft above sea level, and the depth of the trench is \( -23,792 \) ft below sea level. To find the difference, you can add the two values: \[ 14,658 \, \text{ft} - (-23,792 \, \text{ft}) = 14,658 \, \text{ft} + 23,792 \, \text{ft} = 38,450 \, \text{ft} \] So, the difference between the height of the mountain and the depth of the trench is \( 38,450 \, \text{ft} \). --- This part of California features some of the most dramatic elevations and depressions in the contiguous United States, highlighting the interesting geological processes at work. The Sierra Nevada mountain range, where this mountain is located, was formed through tectonic uplift and volcanic activity millions of years ago, creating stunning landscapes that attract outdoor enthusiasts and researchers alike! In real-world applications, understanding such differences in height and depth plays a significant role in various fields such as construction, aviation, and environmental science. For instance, when planning buildings or infrastructure, developers need to take the local topography into account to ensure stability and safety, especially in an area with significant elevation changes like California!