Finding the Height of a Cloud Above a Lake

Full transcript

Imagine you are standing at a point that is exactly 60 metres above the surface of a calm, still lake, and you want to find the height of a cloud floating above you. From that point, you look upward toward the cloud and measure the angle of elevation, which is 30 degrees above the horizontal line of your sight. Now, looking downward into the lake, you can see the reflection of that same cloud, and the angle of depression to that reflection is 60 degrees below the horizontal. Let us define variables: let the height of the cloud above the lake be H metres, and let the horizontal distance from the observer to the point directly below the cloud be D metres. Using trigonometry, from the angle of elevation we get tan 30 equals H minus 60 over D, and from the angle of depression we get tan 60 equals H plus 60 over D, because the reflection is as far below the lake as the cloud is above it. Dividing these two equations and solving, we find that H equals 120 metres, so the cloud is floating at a height of 120 metres above the surface of the lake.