To determine how deep the whale dives when it travels 200 meters at a 20-degree angle below the horizontal, we can utilize some basic trigonometry.
Imagine a right triangle where:
- The hypotenuse (the side opposite the right angle) is the distance the whale travels underwater, which in this case is 200 meters.
- The angle with the horizontal is 20 degrees.
- The opposite side of the triangle represents the depth of the whale.
We are looking for the length of the opposite side, which we can calculate using the sine function:
Sine(Angle) = Opposite Side / Hypotenuse
From this formula, we can rearrange it to find the opposite side (depth):
Opposite Side = Hypotenuse * Sine(Angle)
Now, we can plug in our values:
- Hypotenuse = 200 m
- Angle = 20 degrees
First, calculate the sine of 20 degrees:
sin(20°) ≈ 0.342
Now, substitute the values into the formula:
Depth = 200 m * sin(20°) ≈ 200 m * 0.342
This gives us:
Depth ≈ 68.4 m
Therefore, when the whale dives at an angle of 20 degrees for a distance of 200 meters, it reaches a depth of approximately 68.4 meters.