Kevin and Rob are standing on opposite sides of Edmonton's River Valley. In order to see a boat on the river, Kevin has to look down 32°, and Rob has to look down 38°. The width of the valley is 750m, and the boat is exactly between Kevin and Rob. How much higher is Rob than Kevin?
If their heights are k and r, then
k/375 = sin 32°
r/375 = sin 38°
So, the difference is
r-k = 375(sin38°-sin32°)
To find out how much higher Rob is than Kevin, we need to calculate the height difference between their lines of sight.
Let's start by visualizing the situation. We have Kevin on one side of the river valley, Rob on the other side, and the boat somewhere in the middle.
Since Kevin has to look down 32° to see the boat, we can consider this angle as the angle of depression from Kevin's line of sight towards the boat. Similarly, Rob has to look down 38° from his line of sight towards the boat.
Now, let's consider a diagram to illustrate the situation:
K---------------▼ ▲---------------R
| Boat |
-----------------------------------------------------
River Valley (width = 750m)
In this diagram, "K" represents Kevin, "R" represents Rob, and "▼" and "▲" represent their respective lines of sight towards the boat. The boat is shown between them, denoted as "Boat."
Since we know the width of the river valley is 750m, we can use this information to set up a mathematical relationship between the width and the height difference between Kevin and Rob.
We can use the tangent function to calculate the height difference. The tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle.
For Kevin's line of sight:
tan(32°) = height difference / 750m
For Rob's line of sight:
tan(38°) = height difference / 750m
Let's solve these two equations:
height difference = tan(32°) * 750m
height difference = 0.6249 * 750m
height difference ≈ 468.68m
Therefore, Rob is approximately 468.68 meters higher than Kevin.