a whale comes to the surface to breathe and then dives at an angle of 20 degrees below the horizontal. if the whale continues in a straight line for 150 m, how deep is it, and how far has it traveled horizontally?
51.3
140.9
What is 150*sin20?
How far? what is 150*cos20
51.3m
A whale comes to the surface to breathe and then dives at an angle of 20.0 ∘ below the horizontal .If the whale continues in a straight line for 190 m , how deep is it?
answer gonna be : 190sin(20)= ry = 65.0
190cos(20)=179
Oh whale, that's a deep question! Let's dive right into it.
To find out how deep the whale is, we can use the sine trigonometric function. Since the angle of 20 degrees is measured below the horizontal, we can use the formula:
depth = horizontal distance x sin(angle)
Substituting the values we have, with a horizontal distance of 150 m and an angle of 20 degrees, we can calculate the depth:
depth = 150 m x sin(20°) ≈ 51.55 m
So, the whale is approximately 51.55 meters deep. Quite the impressive dive, I must say!
As for the distance traveled horizontally, it remains the same as the given horizontal distance of 150 meters. So, the whale has traveled 150 meters horizontally without getting lost like a clownfish in a maze.
Keep those aquatic questions coming, and I'll keep clowning around with the answers!
To determine the depth and horizontal distance traveled by the whale, we can use trigonometry. Here's how you can calculate it:
1. Draw a diagram: Draw a right-angled triangle to represent the situation. Label the vertical side as the depth (unknown), the horizontal side as the horizontal distance traveled (unknown), and the hypotenuse as the distance traveled in a straight line (150 m).
2. Use trigonometric ratios: We can use the tangent function, which is defined as the ratio of the opposite side (depth) over the adjacent side (horizontal distance).
tangent(angle) = opposite / adjacent
In this case, the angle is 20 degrees, the opposite side is the depth, and the adjacent side is the horizontal distance traveled.
3. Solve for the depth: Rearrange the equation to isolate the depth.
depth = tangent(angle) * horizontal distance
depth = tangent(20°) * 150 m
Using a calculator, calculate the tangent of 20 degrees. Multiply the result by 150 to find the depth.
4. Solve for the horizontal distance traveled: Use the given value of the horizontal distance, which is 150 m. No calculations are needed for this step.
By following these steps, you can determine the depth and horizontal distance traveled by the whale.