A bowling ball is released at the near right corner of a bowling lane and travels 19.1 m at an angle of 3.0 degrees with respect to the lane's length. he ball reaches the far left corner of the lane, where it knocks down the "7" pin. What is the width of the lane?

sin 3.0o = width/19.1.

Solve for width.

1.001

To find the width of the lane, we need to use some trigonometry and break down the motion of the bowling ball.

First, let's consider the horizontal distance the ball travels. Since it starts at the near right corner and reaches the far left corner, the ball travels the full width of the lane.

Next, let's find the horizontal distance the ball travels using trigonometry. We can use the angle (3.0 degrees) and the distance traveled (19.1 m) to find the horizontal component of the ball's motion.

The horizontal distance (d) can be calculated using the formula:

d = distance traveled * cos(angle)

In this case, d = 19.1 m * cos(3.0 degrees)

Now, let's calculate the value of d:

d = 19.1 m * cos(3.0 degrees)
≈ 19.1 m * 0.9986 (cosine of 3.0 degrees)
≈ 19.0676 m

So, the horizontal distance the ball travels is approximately 19.0676 meters.

Since the horizontal distance is the same as the width of the lane, the width of the lane is approximately 19.0676 meters.